Benoit Collins

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Name
Benoit Collins
URL
https://www.math.kyoto-u.ac.jp/~collins/
Affiliation
Kyoto University
Section
Graduate School of Science

Research Areas

 
 

Academic & Professional Experience

 
Apr 2014
 - 
Today
Kyoto University
 

Education

 
Sep 1996
 - 
Aug 2000
Ecole Normale Supérieure de Paris
 

Published Papers

 
Michael Brannan, Beno{\^{\i}}t Collins
Communications in Mathematical Physics      Mar 2018   [Refereed]
Benoit Collins, Pierre Yves Gaudreau Lamarre
Advances in Applied Mathematics   83 47   Feb 2017   [Refereed]
Benoît Collins, Motohisa Fukuda, Ion Nechita
Journal of Operator Theory   73(2) 333-360   Jan 2015   [Refereed]
© by THETA, 2015. We study the asymptotic behavior of the output states of sequences of quantum channels. Under a natural assumption, we show that the output set converges to a compact convex set, clarifying and substantially generalizing results ...
Belinschi S.T, Collins B, Nechita I.
Communications in Mathematical Physics   1-25   2016   [Refereed]
Bercovici Hari, Collins Benoit, Dykema Ken, Li Wing Sue
Bulletin des Sciences Mathématiques   139(4) 400-419   Jan 2015   [Refereed]
© 2014 Elsevier Masson SAS. We characterize in terms of inequalities the possible generalized singular numbers of a product AB of operators A and B having given generalized singular numbers, in an arbitrary finite von Neumann algebra. We also solv...
Benoît Collins, Benoît Collins, Benoît Collins, Piotr Gawron, Alexander E. Litvak, Karol Zyczkowski, Karol Zyczkowski
Journal of Mathematical Analysis and Applications   418(1) 516-533   Oct 2014   [Refereed]
We analyze the numerical range of high-dimensional random matrices, obtaining limit results and corresponding quantitative estimates in the non-limit case. For a large class of random matrices their numerical range is shown to converge to a disc. ...
Benoît Collins, Motohisa Fukuda, Ping Zhong
International Journal of Mathematics   26(1) 1550002, 20   Jan 2015   [Refereed]
© 2015 World Scientific Publishing Company. The free contraction norm (or the (t)-norm) was introduced by Belinschi, Collins and Nechita as a tool to compute the typical location of the collection of singular values associated to a random subspace...
Bercovici H, Collins B, Dykema K, Li W.S.
Bulletin des Sciences Mathematiques   139(4) 400-419   2015   [Refereed]
Benoît Collins, Benoît Collins, Benoît Collins, Ion Nechita, Karol Zyczkowski, Karol Zyczkowski
Journal of Physics A: Mathematical and Theoretical   46(30) 305302-1   Aug 2013   [Refereed]
Random pure states of multi-partite quantum systems, associated with arbitrary graphs, are investigated. Each vertex of the graph represents a generic interaction between subsystems, described by a random unitary matrix distributed according to th...
Benoît Collins, Benoît Collins, Benoît Collins, Sho Matsumoto, Nadia Saad
Journal of Multivariate Analysis   126 1-13   Apr 2014   [Refereed]
We consider random matrices that have invariance properties under the action of unitary groups (either a left-right invariance, or a conjugacy invariance), and we give formulas for moments in terms of functions of eigenvalues. Our main tool is the...
Benoît Collins, Benoît Collins, Benoît Collins, Todd Kemp
Journal of Functional Analysis   266(4) 1988-2052   Feb 2014   [Refereed]
We study the liberation process for projections: (p,q){mapping}(pt,q)=(utput *,q) where ut is a free unitary Brownian motion freely independent from {p, q}. Its action on the operator-valued angle qptq between the projections induces a flow on the...
Collins Beno\^\\it, Male Camille
Ann. Sci. Éc. Norm. Supér. (4)   47(1) 147-163   Jan 2014   [Refereed]
In this paper, we are interested in sequences of q-tuple of N × N random matrices having a strong limiting distribution (i.e., given any non-commutative polynomial in the matrices and their conjugate transpose, its normalized trace and its norm co...
Benoît Collins,Hun Hee Lee, Piotr Sniady
Studia Mathematica   220(3) 221-241   Jan 2014   [Refereed]
© Instytut Matematyczny PAN, 2014 We give universal upper bounds on the relative dimensions of isotypic components of a tensor product of representations of the linear group GL(n) and universal upper bounds on the relative dimensions of irreducibl...
Benoît Collins, Carlos E. González-Guillén, Carlos E. González-Guillén, David Pérez-García, David Pérez-García
Communications in Mathematical Physics   320(3) 663-677   Jun 2013   [Refereed]
Using random matrix techniques and the theory of Matrix Product States we show that reduced density matrices of quantum spin chains have generically maximum entropy. © 2013 Springer-Verlag Berlin Heidelberg.
Collins B, Male C.
Annales Scientifiques de l'Ecole Normale Superieure   47(1) 147-163   2014   [Refereed]
Collins B, Gawron P, Litvak A.E, Zyczkowski K.
Journal of Mathematical Analysis and Applications   418(1) 516-533   2014   [Refereed]
Teodor Banica, Julien Bichon, Benoît Collins, Stephen Curran
Communications in Algebra   41(2) 656-665   Feb 2013   [Refereed]
We prove that the quantum group inclusion On ⊂ O* n is "maximal," where On is the usual orthogonal group and O* n is the half-liberated orthogonal quantum group, in the sense that there is no intermediate compact quantum group On ⊂ G ⊂ O* n. In or...
Collins B, Kemp T.
Journal of Functional Analysis   266(4) 1988-2052   2014   [Refereed]
Adamczak R, Barone P, Bose A, Gangopadhyay S, Saha K, Cafasso M, Cheng X, Singer A, Collins B, Fukuda M, other
evaluation   2 1350003   2013   [Refereed]
Collins B, Lee H.H, ͆niady P.
Studia Mathematica   220(3) 221-241   2014   [Refereed]
Benoit Collins, Motohisa Fukuda, Ion Nechita
Random Matrices: Theory Appl. 02, 1250018 (2013)   2(1) 1250018, 36   Aug 2012   [Refereed]
In this paper, we study the behaviour of the output of pure entangled states
after being transformed by a product of conjugate random unitary channels. This
study is motivated by the counterexamples by Hastings and Hayden-Winter to the
additivity ...
Collins B, Matsumoto S, Saad N.
Journal of Multivariate Analysis   126 1-13   2014   [Refereed]
Serban Belinschi, Serban Belinschi, Benoît Collins, Benoît Collins, Ion Nechita
Inventiones Mathematicae   190(3) 647-697   Feb 2012   [Refereed]
Given two positive integers n and k and a parameter t ∈ (0, 1), we choose at random a vector subspace V n⊂ℂ k⊗ℂ n of dimension N ~ tnk. We show that the set of k-tuples of singular values of all unit vectors in V n fills asymptotically (as n tends...
Hari Bercovici, Benoit Collins, Ken Dykema, Wing Suet Li
   Jun 2013
We characterize in terms of inequalities the possible generalized singular
numbers of a product AB of operators A and B having given generalized singular
numbers, in an arbitrary finite von Neumann algebra. We also solve the
analogous problem in m...
Collins Beno\^\\it, Nechita Ion, \.Zyczkowski Karol
J. Phys. A   46(30) 305302, 18   2013   [Refereed]
Benoit Collins, Sho Matsumoto, Nadia Saad
   May 2012
We consider random matrices that have invariance properties under the action
of unitary groups (either a left-right invariance, or a conjugacy invariance),
and we give formulas for moments in terms of functions of eigenvalues. Our main
tool is the...
Benoît Collins, Motohisa Fukuda, Ion Nechita
Journal of Mathematical Physics   53    Mar 2012   [Refereed]
We consider the image of some classes of bipartite quantum states under a tensor product of random quantum channels. Depending on natural assumptions that we make on the states, the eigenvalues of their outputs have new properties which we describ...
Collins B, Dykema K.J
New York Journal of Mathematics   17 437-444   Sep 2011   [Refereed]
We prove by a counterexample that asymptotic quantum Horn bodies are not convex in general.
Benoit Collins, Ion Nechita, Deping Ye
Random Matrices: Theory Appl. 01, 1250002 (2012)      Aug 2011
In this paper, we first obtain an algebraic formula for the moments of a
centered Wishart matrix, and apply it to obtain new convergence results in the
large dimension limit when both parameters of the distribution tend to infinity
at different sp...
Karol Zyczkowski, Karol Zyczkowski, Karol A. Penson, Ion Nechita, Ion Nechita, Benoît Collins
Journal of Mathematical Physics   52    Jun 2011
We study various methods to generate ensembles of random density matrices of a fixed size N, obtained by partial trace of pure states on composite systems. Structured ensembles of random pure states, invariant with respect to local unitary transfo...
Benoît Collins, Benoît Collins, Ion Nechita
Annals of Applied Probability   21 1136-1179   Jun 2011
In this paper, we present applications of the calculus developed in Collins and Nechita [Comm. Math. Phys. 297 (2010) 345-370] and obtain an exact formula for the moments of random quantum channels whose input is a pure state thanks to Gaussianiza...
Teodor Banica, Benoit Collins, Jean Marc Schlenker
Journal of Combinatorial Theory. Series A   118 778-795   Apr 2011   [Refereed]
We consider integrals of type ∫Onu11a1...u1nanu21b1...u2nbndu, with respect to the Haar measure on the orthogonal group. We establish several remarkable invariance properties satisfied by such integrals, by using combinatorial methods. We present ...
T. Banica, S. T. Belinschi, M. Capitaine, B. Collins
Canadian Journal of Mathematics   63 3-37   Feb 2011
We introduce and study a remarkable family of real probability measures π that we call free Bessel laws. These are related to the free Poisson law π via the formulae π = π and π = π. Our study includes definition and basic properties, analytic asp...
Benoît Collins, Benoît Collins, Benoît Collins, Ion Nechita
Advances in Mathematics   226 1181-1201   Jan 2011
In this paper we obtain new bounds for the minimum output entropies of random quantum channels. These bounds rely on random matrix techniques arising from free probability theory. We then revisit the counterexamples developed by Hayden and Winter ...
Collins Beno\^\\it, Dykema Kenneth J
Münster J. Math.   4 101   2011   [Refereed]
Teodor Banica, Benoît Collins, Jean Marc Schlenker
Indiana University Mathematics Journal   59 839-856   Dec 2010
For U ∈ O(N) we have ∥U∥1 ≤ N √N, with equality if and only if U = H/ √N, with H Hadamard matrix. Motivated by this remark, we discuss in this paper the algebraic and analytic aspects of the computation of the maximum of the 1-norm on O(N). The ma...
Benot Collins, Benot Collins, Ion Nechita, Karol Zyczkowski, Karol Zyczkowski
Journal of Physics A: Mathematical and Theoretical   43    Jun 2010
For any graph consisting of k vertices and m edges we construct an ensemble of random pure quantum states which describe a system composed of 2m subsystems. Each edge of the graph represents a bipartite, maximally entangled state. Each vertex repr...
Benoît Collins, Benoît Collins, Kenneth J. Dykema, Francisco Torres-Ayala
Journal of Statistical Physics   139 779-799   Jun 2010
We show that the polynomial Sm,k(A,B), that is the sum of all words in noncommuting variables A and B having length m and exactly k letters equal to B, is not equal to a sum of commutators and Hermitian squares in the algebra R〈X,Y〉, where X2=A an...
Benoît Collins, Ion Nechita
Entropy   12 1612-1631   Jun 2010   [Refereed]
Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models of relev...
Benoit Collins, Ken Dykema
Münster J. Math. 4 (2011), 101--118      Mar 2010
We show that free products of sofic groups with amalgamation over
monotileably amenable subgroups are sofic. Consequently, so are HNN extensions
of sofic groups relative to homomorphisms of monotileably amenable subgroups.
We also show that famili...
Benoît Collins, Benoît Collins, Ion Nechita
Communications in Mathematical Physics   297 345-370   Mar 2010   [Refereed]
This paper is the first of a series where we study quantum channels from the random matrix point of view. We develop a graphical tool that allows us to compute the expected moments of the output of a random quantum channel. As an application, we s...
H. Bercovici, B. Collins, B. Collins, K. Dykema, W. S. Li, D. Timotin
Journal of Functional Analysis   258 1579-1627   Mar 2010
The intersection ring of a complex Grassmann manifold is generated by Schubert varieties, and its structure is governed by the Littlewood-Richardson rule. Given three Schubert varieties S1, S2, S3 with intersection number equal to one, we show how...
Benoît Collins, Benoît Collins, Sho Matsumoto
Journal of Mathematical Physics   50    Dec 2009
We give a Fourier-type formula for computing the orthogonal Weingarten formula. The Weingarten calculus was introduced as a systematic method to compute integrals of polynomials with respect to Haar measure over classical groups. Although a Fourie...
Teodor Banica, Benoit Collins, Paul Zinn-Justin
International Mathematics Research Notices   2009 3286-3309   Dec 2009
We compute the spectral measure of the standard generators u ij of the Wang algebra A o(n). We show, in particular, that this measure has support [-2/√n + 2, 2/√ n + 2], and that it has no atoms. The computation is done by using various techniques...
Benoit Collîns, Piotr Śniady
   Nov 2009   [Refereed]
We study asymptotics of representations of the unitary groups U(n) in the
limit as n tends to infinity and we show that in many aspects they behave like
large random matrices. In particular, we prove that the highest weight of a
random irreducible...
Teodor Banica, Benoit Collins, Jean-Marc Schlenker
J. Combin. Theory Ser. A 118 (2011), 778-795      Oct 2009
We consider integrals of type Tex, with respect to the Haar measure
on the orthogonal group. We establish several remarkable invariance properties
satisfied by such integrals, by ...
Benoît Collins, Benoît Collins, Alice Guionnet, Edouard Maurel-Segala
Advances in Mathematics   222 172-215   Sep 2009
In this paper, we prove that in small parameter regions, arbitrary unitary matrix integrals converge in the large N limit and match their formal expansion. Secondly we give a combinatorial model for our matrix integral asymptotics and investigate ...
Benoit Collins, Ken Dykema
   Jun 2009
We prove by a counterexample that asymptotic quantum Horn bodies are not
convex in general.
Benoît Collins, Benoît Collins, Piotr Śniady
Transactions of the American Mathematical Society   361 3269-3287   Jun 2009
We study the asymptotics of representations of a fixed compact Lie group. We prove that the limit behavior of a sequence of such representations can be described in terms of certain random matrices; in particular operations on representations (for...
Collins Beno\^\\it, Dykema Ke
Oper. Matrices   3(1) 1-40   Mar 2009   [Refereed]
We consider the analogues of the Horn inequalities in finite von Neumann algebras, which concern the possible spectral distributions of sums a+b of self-adjoint elements a and b in a finite von Neumann algebra. It is an open question whether all o...
Benoît Collins, Benoît Collins, Johannes Härtel, Andreas Thom
Comptes Rendus Mathematique   347 271-276   Mar 2009
We compute the Hochschild homology of the free orthogonal quantum group Ao (n). We show that it satisfies Poincaré duality and should be considered to be a 3-dimensional object. We then use recent results of R. Vergnioux to derive results about th...
Teodor Banica, Benoit Collins, Jean-Marc Schlenker
Indiana Univ. Math. J. 59 (2010), 839-856      Jan 2009
For Tex we have Tex, with equality if and only if
Tex, with Tex Hadamard matrix. Motivated by this remark, we discuss
in this paper the algebraic and analytic aspects of the computation of the
maximum of the ...
Collins B, Dykema K
Operators and Matrices   3(1) 1-40   2009   [Refereed]
Collins B, Dykema K
New York Journal of Mathematics   14 617-641   Dec 2008   [Refereed]
We show that Connes' embedding problem for II1-factors is equivalent to a statement about distributions of sums of self-adjoint operators with matrix coefficients. This is an application of a linearization result for finite von Neumann algebras, w...
Teodor Banica, Benoît Collins, Benoît Collins
Journal of Geometry and Physics   58 942-961   Aug 2008
We prove that the Pauli representation of the quantum permutation algebra As (4) is faithful. This provides the second known model for a free quantum algebra. We use this model for performing some computations and show that, at the level of the la...
Benoît Collins, Benoît Collins, Benoît Collins, Michael Stolz, Michael Stolz
Annals of Probability   36 876-895   May 2008
We study random vectors of the form (Tr(A(1)V),..., Tr(A (r) V)), where V is a uniformly distributed element of a matrix version of a classical compact symmetric space, and the A(ν) are deterministic parameter matrices. We show that for increasing...
Collins Beno\^\\it, Dykema Ke
New York J. Math.   14 617   2008   [Refereed]
Collins B, Mingo J.A, Śniady P, Speicher R
Documenta Mathematica   12 1-70   Dec 2007   [Refereed]
We extend the relation between random matrices and free probability theory from the level of expectations to the level of all correlation functions (which are classical cumulants of traces of products of the matrices). We introduce the notion of "...
Benoit Collins, Ken Dykema
Oper. Matrices 3 (2009), 1-40      Nov 2007
We consider the analogues of the Horn inequalities in finite von Neumann
algebras, which concern the possible spectral distributions of sums Tex of
self--adjoint elements Tex and Tex in a finite von Neumann algebra. It is an
open question whethe...
Teodor Banica, Serban Belinschi, Mireille Capitaine, Benoit Collins
Canad. J. Math. 63 (2011), 3-37      Nov 2007
We introduce and study a remarkable family of real probability measures
Tex, that we call free Bessel laws. These are related to the free
Poisson law Tex via the formulae Tex and
Tex. Our s...
Benoit Collins, Ken Dykema
New York J. Math. 14 (2008), 617-641      Jun 2007
We show that Connes' embedding problem for II_1-factors is equivalent to a
statement about distributions of sums of self-adjoint operators with matrix
coefficients. This is an application of a linearization result for finite von
Neumann algebras, ...
Teodor Banica, Benoît Collins
Publications of the Research Institute for Mathematical Sciences   43 277-302   Jun 2007
We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures. © 2007 Resear...
Benoît Collins, Piotr Śniady
Annales de l'institut Henri Poincare (B) Probability and Statistics   43 139-146   Mar 2007
We study asymptotics of the Itzykson-Zuber integrals in the scaling when one of the matrices has a small rank compared to the full rank. We show that the result is basically the same as in the case when one of the matrices has a fixed rank. In thi...
Teodor Banica, Julien Bichon, Benoit Collins
J. Ramanujan Math. Soc. 22 (2007), 345-384      Jan 2007
We consider the hypercube in Tex, and show that its quantum
symmetry group is a Tex-deformation of Tex at Tex. Then we consider the
graph formed by Tex segments, and show that its quantum symmetry group is free
in some natural sense...
Teodor Banica, Teodor Banica, Benoît Collins
Journal of Functional Analysis   242 641-657   Jan 2007
We find a combinatorial formula for the Haar measure of quantum permutation groups. This leads to a dynamic formula for laws of diagonal coefficients, explaining the Poisson/free Poisson convergence result for characters. © 2006 Elsevier Inc. All ...
Banica Teodor, Bichon Julien, Collins Benoit, Bozejko M, Krystek A, Mlotkowski W, Wysoczanski
78 13-34   2007   [Refereed]
Teodor Banica, Julien Bichon, Benoit Collins
Banach Center Publ. 78 (2007), 13-34      Dec 2006
This is a presentation of recent work on quantum permutation groups.
Contains: a short introduction to operator algebras and Hopf algebras; quantum
permutation groups, and their basic properties; diagrams, integration formulae,
asymptotic laws, ma...
Benoît Collins, Piotr Śniady
Communications in Mathematical Physics   264 773-795   Jun 2006
We revisit the work of the first named author and using simpler algebraic arguments we calculate integrals of polynomial functions with respect to the Haar measure on the unitary group U(d). The previous result provided exact formulas only for 2d ...
Benoît Collins, Benoît Collins
Probability Theory and Related Fields   133 315-344   Nov 2005
We consider the product of two independent randomly rotated projectors. The square of its radial part turns out to be distributed as a Jacobi ensemble. We study its global and local properties in the large dimension scaling relevant to free probab...
Benoît Collins
Annales de l'institut Henri Poincare (B) Probability and Statistics   40 367-384   May 2004
In this paper we define a general setting for Martin boundary theory associated to quantum random walks, and prove a representation theorem. We show that in the dual of a simply connected Lie subgroup of U(n), the extremal Martin boundary is homeo...
Benoit Collins
Int. Math. Res. Not., (17):953-982, 2003.      May 2002
We consider integrals on unitary groups Tex of the form
\int_{U_d}U_{i_1j_1}... U_{i_qj_q}U^*_{j'_{1}i'_{1}} ...
U^*_{j'_{q'}i'_{q'}}dU
We give an explicit formula in terms of characters of symmetric groups and
Schur functions, which allow...

Misc

 
Benoit Collins
   Mar 2016
We give a simple and conceptual proof of the fact that random unitary
channels yield violation of the Minimum Output Entropy additivity. The proof
relies on strong convergence of random unitary matrices and Haagerup's
inequality.
Benoit Collins, Takahiro Hasebe, Noriyoshi Sakuma
   Dec 2015
We study the eigenvalues of polynomials of large random matrices which have
only discrete spectra. Our model is closely related to and motivated by spiked
random matrices, and in particular to a recent result of Shlyakhtenko in which
asymptotic in...
Benoit Collins, Ion Nechita
Journal of Mathematical Physics 57, 015215 (2016)      Sep 2015
The purpose of this review article is to present some of the latest
developments using random techniques, and in particular, random matrix
techniques in quantum information theory. Our review is a blend of a rather
exhaustive review, combined with...
Benoit Collins, Motohisa Fukuda, Ion Nechita
   Nov 2013
We study the asymptotic behavior of the output states of sequences of quantum
channels. Under a natural assumption, we show that the output set converges to
a compact convex set, clarifying and substantially generalizing results in
[BCN13]. Random...
Cioppa Timothy, Collins Benoi
arXiv preprint arXiv:1307.4766      Jul 2013   [Refereed]
In this paper, we establish an explicit isomorphism between the symmetric
group algebra and the path algebra of the Young graph. Specifically, we
construct a family of matrix units in the group algebra. As a main application
of this construction, ...
Collins Beno\^\\it, McDonald David, Saad Nadi
arXiv preprint arXiv:1306.5510      Jun 2013   [Refereed]
In this paper, we obtain a property of the expectation of the inverse of
compound Wishart matrices which results from their orthogonal invariance. Using
this property as well as results from random matrix theory (RMT), we derive the
asymptotic eff...
Benoit Collins, James A. Mingo, Piotr Sniady, Roland Speicher
Doc. Math. 12 (2007), 1-70 (electronic)      Jun 2006
We extend the relation between random matrices and free probability theory
from the level of expectations to the level of all correlation functions (which
are classical cumulants of traces of products of the matrices). We introduce
the notion of "...
Benoit Collins, Alice Guionnet, Edouard Maurel-Segala
   Aug 2006
In this paper, we prove that in small parameter regions, arbitrary unitary
matrix integrals converge in the large Tex limit and match their formal
expansion. Secondly we give a combinatorial model for our matrix integral
asymptotics and investigat...
Benoit Collins, Camille Male
Annales scientifiques de l'ENS (4) 47, fascicule 1 (2014), 147-163      May 2011
In this paper, we are interested in sequences of q-tuple of N-by-N random
matrices having a strong limiting distribution (i.e. given any non-commutative
polynomial in the matrices and their conjugate transpose, its normalized trace
and its norm co...
Benoit Collins, Todd Kemp
   Nov 2012
We study the liberation process for projections: Tex where Tex is a free unitary Brownian motion freely
independent from Tex. Its action on the operator-valued angle Tex
between the projections indu...
Teodor Banica, Benoit Collins
J. Funct. Anal. 242 (2007), 641-657      Jun 2006
We find a combinatorial formula for the Haar measure of quantum permutation
groups. This leads to a dynamic formula for laws of diagonal coefficients,
explaining the Poisson/free Poisson convergence result for characters.
Teodor Banica, Benoit Collins
Publ. Res. Inst. Math. Sci. 43 (2007), 277-302      Nov 2005
We find a combinatorial formula for the Haar functional of the orthogonal and
unitary quantum groups. As an application, we consider diagonal coefficients of
the fundamental representation, and we investigate their spectral measures.
Benoit Collins
Annales de l'IHP, Vol 40, 3:367--384 (2004).      Nov 2002
In this paper we define a general setting for Martin boundary theory
associated to quantum random walks, and prove a general representation theorem.
We show that in the dual of a simply connected Lie subgroup of U(n), the
extremal Martin boundary ...

Conference Activities & Talks

 
k-positive maps [Invited]
Benoit Collins
MFO, free probability, Oberwolfach   9 Jun 2015   
Unitary Valued Brownian Motion [Invited]
Benoit Collins
Queen's free probability seminar   10 Mar 2015   
Random positive maps [Invited]
Benoit Collins
Random matrices and their applications, Hong Kong   19 Jan 2015   
Weingarten calculus and applications [Invited]
Benoit Collins
Winter school on Operator Spaces, Noncommutative Probability and Quantum Groups, Metabief   8 Dec 2014   
Random positive maps [Invited]
Benoit Collins
Colloquium, Kolkata   25 Sep 2014   
random tensors and asymptotic freeness [Invited]
Benoit Collins
ESI workshop, Austria   17 Jul 2014   
MOE additivity violation via free probability theory [Invited]
Benoit Collins
Colloquio sul, Florianopolis, Brazil   29 Apr 2014   
Numerical range for random matrices
Benoit Collins
Queen's free probability seminar   15 Feb 2014   
Describing exchangeable SU(n) invariant separable states
Benoit Collins
KOAS   22 Apr 2014   
numerical range of random matrices [Invited]
Benoit Collins
Kansai seminar, Kinosaki   11 Dec 2013   
Violation of the MOE additivity via free probability [Invited]
Benoit Collins
Seoul National University Operator Algebra seminar   21 Nov 2013   
Free probability and QIT [Invited]
Benoit Collins
Kyoto University colloquium   13 Nov 2013   
QIT and Free probability
Benoit Collins
Special colloquium, Tohoku University   12 Nov 2013   
Quantum channels and free probability [Invited]
Benoit Collins
JSP-DST seminar, Tokyo University   25 Oct 2013   
Law of large numbers for eigenvalues of random subspaces
Benoit Collins
14 Mar 2013   
colloquium [Invited]
Benoit Collins
1 Feb 2013   
RANDOM MATRICES, FREE PROBABILITY AND QUANTUM INFORMATION THEORY [Invited]
Benoit Collins
Quantum Information Theory talk, Perimeter Institute   31 Jan 2013   
Norm convergence of unitary random matrix models and quantum information theory [Invited]
Benoit Collins
AMS SPECIAL SESSION ON THE PROGRESS IN FREE PROBABILITY AND FREE ANALYSIS   11 Jan 2013   
Random matrices, free probability and quantum information THEORY [Invited]
Benoit Collins
Geometry Seminar, Tohoku University   15 Nov 2012   
Mouvements browniens non commutatifs
Benoit Collins
Séminaire d'Analyse Harmonique Non Commutative, Université de Caen Basse-Normandie   24 Oct 2012   
Probability seminar
Benoit Collins
Probability Seminar   1 Oct 2012   
Liberation of projections [Invited]
Benoit Collins
Minisymposium on Free Probability and Random Matrices, Saarland University   17 Sep 2012   
Free probability techniques in quantum information theory [Invited]
Benoit Collins
Workshop on Quantum Probabilistic Symmetries, Aberystwyth University   3 Sep 2012   
Free probability and QIT [Invited]
Benoit Collins
inauguration du pole d'excellence   1 Sep 2012   
Random matrices, free probability and quantum information THEORY [Invited]
Benoit Collins
RMT and statistics   1 Jul 2012   
talk [Invited]
Benoit Collins
colloquium Germany Leipzig   1 Jun 2012   
Non-Commutative Brownian Motions [Invited]
Benoit Collins
Probabilistic Methods in Quantum Mechanics, University Claude Bernard Lyon 1   6 May 2012   
Matrices aléatoires et information quantique [Invited]
Benoit Collins
Séminaire de Probabilités-Statistiques, Laboratoire de Mathématiques de Versailles   10 Apr 2012   
Norm convergence for unitary random matrices [Invited]
Benoit Collins
EPSRC Symposium Workshop - Interacting particle systems, growth models and random matrices, University of Warwick   21 Mar 2012   
talk [Invited]
Benoit Collins
Quantum Information Theory Seminar, ETH Zurich   21 Mar 2012   
talk [Invited]
Benoit Collins
RMT and free probability theory California, United States Berkeley   1 Mar 2012   
quantum symmetries [Invited]
Benoit Collins
quantum symmetries workshop   1 Mar 2012   
Random quantum channels [Invited]
Benoit Collins
Operator structures in quantum information theory, Banff International Research Station Alberta, Canada Banff   27 Feb 2012   
talk [Invited]
Benoit Collins
seminaire de probabilites France Toulouse   1 Feb 2012   
talk [Invited]
Benoit Collins
Centre International de Rencontres Mathématiques France Marseille   15 Jan 2012   
talk [Invited]
Benoit Collins
Operator Algebra seminar Korea, Republic of Cheongju   15 Nov 2011   
talk [Invited]
Benoit Collins
OA/FA meeting Japan Okinawa   1 Nov 2011   
New results in Free Probability theory and applications to Quantum Information theory [Invited]
Benoit Collins
Kyoto Operator Algebra Seminar, Research Institute for Mathematical Sciences Japan Kyoto   12 Oct 2011   
Random matrices, representations of GL(n) and free probability of higher order [Invited]
Benoit Collins
Large N-limit of random multi-matrix systems, von Neumann algebras and free probability, The Erwin Schrodinger International Institute for Mathematical Physics   21 Apr 2011   
talk [Invited]
Benoit Collins
RMT/stats conference Minnesota, United States Minneapolis   1 Apr 2011   
talk [Invited]
Benoit Collins
Large N-limit of random multi-matrix systems, von Neumann algebras and free probability, The Erwin Schrodinger International Institute for Mathematical Physics   1 Feb 2011   
Computational Approach to Mathematical Problems - Riemann Hypothesis [Invited]
Benoit Collins
Japanese-French Frontiers of Science, Japan Society for the Promotion of Science Japan Tokyo   21 Jan 2011   
talk [Invited]
Benoit Collins
Seminar of Operator Algebras, University of Copenhagen   24 Nov 2010   
talk [Invited]
Benoit Collins
Quantum Information Theory, Institut Mittag-Leffler   1 Nov 2010   
Free probability and entropy additivity problems for Quantum information theory [Invited]
Benoit Collins
Operator Algebra Seminar, University of Tokyo   21 Oct 2010   
Courses on quantum groups, free probability and non-commutative geometry [Invited]
Benoit Collins
Groupes quantiques et géométrie non commutative, Centre International de Rencontres Mathématiques   27 Sep 2010   
Higher order freeness and asymptotic representations of unitary groups [Invited]
Benoit Collins
Seminar on Asymptotic Representation Theory, Nagoya University   16 Sep 2010   

Association Memberships

 
 

Research Grants & Projects

 
Random Matrix Theory and applications to Quantum Information Theory
JSPS: 
Project Year: Apr 2017 - Mar 2021    Investigator(s): Benoit Collins
Applications of Quantum Groups and Representation Theory to Quantum Information Theory
JSPS: 
Project Year: Jul 2017 - Mar 2020    Investigator(s): Benoit Collins
Random Matrix Theory and its applications(国際共同研究強化)
JSPS: 
Project Year: Apr 2016 - Oct 2018    Investigator(s): Benoit Collins
Random Matrix Theory and its applications
JSPS: 
Project Year: Apr 2014 - Mar 2018    Investigator(s): Benoit Collins