J-GLOBALへ         更新日: 19/09/24 14:29






京都大学  Department of Advanced Mathematical Sciences, Graduate School of Informatics Associate Professor
University of Warwick Department of Statistics Reader
University of Warwick Department of Statistics Associate Professor
University of Warwick Department of Statistics Assistant Professor
University of Warwick Department of Statistics Postdoctoral Research Fellow


Journal of Mathematical Physics   60(083301)    2019年   [査読有り]
RIMS Kokyuroku   2116 203-212   2019年   [査読有り]
David A. Croydon, Tsuyoshi Kato, Makiko Sasada, Satoshi Tsujimoto
The box-ball system (BBS), introduced by Takahashi and Satsuma in 1990, is a
cellular automaton that exhibits solitonic behaviour. In this article, we study
the BBS when started from a random two-sided infinite particle configuration.
For such a m...
D. A. Croydon
Ann. Inst. H. Poincare Probab. Statist.   54(4) 1939-1968   2018年   [査読有り]
We establish that if a sequence of spaces equipped with resistance metrics
and measures converge with respect to the Gromov-Hausdorff-vague topology, and
a certain non-explosion condition is satisfied, then the associated stochastic
processes also...
David Croydon, Ben Hambly, Takashi Kumagai
Stoch. Proc. Appl.      2017年11月   [査読有り]
Quenched and annealed heat kernel estimates are established for
Fontes-Isopi-Newman (FIN) processes on spaces equipped with a resistance form.
These results are new even in the case of the one-dimensional FIN diffusion,
and also apply to fractals ...
Philippe H. A. Charmoy, David A. Croydon, Ben M. Hambly
Trans. Amer. Math. Soc.   369 8967-9013   2017年   [査読有り]
We discuss the spectral asymptotics of some open subsets of the real line
with random fractal boundary and of a random fractal, the continuum random
tree. In the case of open subsets with random fractal boundary we establish the
existence of the s...
David Croydon, Stephen Muirhead
Probab. Theory Related Fields 168 (2017), 269-315      2017年   [査読有り]
We consider the quenched localisation of the Bouchaud trap model on the
positive integers in the case that the trap distribution has a slowly varying
tail at infinity. Our main result is that for each Tex
there exists a slowly...
David A. Croydon
RIMS Kokyuroku   2030 1-8   2017年
We introduce and summarise results from the recent paper `Scaling limits of
stochastic processes associated with resistance forms', and also applications
from `Time-changes of stochastic processes associated with resistance forms',
which was writt...
D. A. Croydon, B. M. Hambly, T. Kumagai
Electron. J. Probab.   22(82) 1-41   2017年   [査読有り]
Given a sequence of resistance forms that converges with respect to the
Gromov-Hausdorff-vague topology and satisfies a uniform volume doubling
condition, we show the convergence of corresponding Brownian motions and local
times. As a corollary of...
M. T. Barlow, D. A. Croydon, T. Kumagai
Annals of Probability 2017, Vol. 45, No. 1, 4-55      2017年   [査読有り]
The first main result of this paper is that the law of the (rescaled)
two-dimensional uniform spanning tree is tight in a space whose elements are
measured, rooted real trees continuously embedded into Euclidean space. Various
properties of the in...
David Croydon, Stephen Muirhead
RIMS Kokyuroku Bessatsu   B59 305-320   2016年   [査読有り]
This article describes the quenched localisation behaviour of the Bouchaud
trap model on the integers with regularly varying traps. In particular, it
establishes that for almost every trapping landscape there exist arbitrarily
large times at which...
Zhen-Qing Chen, David A. Croydon, Takashi Kumagai
Annals of Probability 2015, Vol. 43, No. 4, 1594-1642      2015年   [査読有り]
Via a Dirichlet form extension theorem and making full use of two-sided heat
kernel estimates, we establish quenched invariance principles for random walks
in random environments with a boundary. In particular, we prove that the random
walk on a s...
David Croydon, Stephen Muirhead
Stoch. Proc. Appl 125(5) (2015), 1980-2009      2015年   [査読有り]
We consider the Bouchaud trap model on the integers in the case that the trap
distribution has a slowly varying tail at infinity. Our main result is a
functional limit theorem for the model under the annealed law, analogous to the
functional limit...
David A. Croydon
Trans. Lond. Math. Soc.   2(1) 57-79   2015年   [査読有り]
In this article, universal concentration estimates are established for the
local times of random walks on weighted graphs in terms of the resistance
metric. As a particular application of these, a modulus of continuity for local
times is provided ...
David A. Croydon, Alexander Fribergh, Takashi Kumagai
Probab. Theory Related Fields   157(1) 453-507   2013年   [査読有り]
We consider the biased random walk on a critical Galton-Watson tree
conditioned to survive, and confirm that this model with trapping belongs to
the same universality class as certain one-dimensional trapping models with
slowly-varying tails. Inde...
David Croydon, Ben Hambly, Takashi Kumagai
Electronic Journal of Probability 17 (2012), paper no. 3      2012年   [査読有り]
We establish conditions on sequences of graphs which ensure that the mixing
times of the random walks on the graphs in the sequence converge. The main
assumption is that the graphs, associated measures and heat kernels converge in
a suitable Gromo...
David Croydon, Ben Hambly
Electron. J. Probab.   15(2) 1772-1801   2010年   [査読有り]
We calculate the mean and almost-sure leading order behaviour of the high
frequency asymptotics of the eigenvalue counting function associated with the
natural Dirichlet form on Tex-stable trees, which lead in turn to
short-time heat kernel a...
David A. Croydon, Takashi Kumagai
Electronic Journal of Probability 13 (2008) 1419-1441      2008年   [査読有り]
We establish a variety of properties of the discrete time simple random walk
on a Galton-Watson tree conditioned to survive when the offspring distribution,
Tex say, is in the domain of attraction of a stable law with index
Tex. In pa...
D. A. Croydon, B. M. Hambly
Stochastic Processes and their Applications 118 (2008), no. 5, 730-754      2008年   [査読有り]
We use the random self-similarity of the continuum random tree to show that
it is homeomorphic to a post-critically finite self-similar fractal equipped
with a random self-similar metric. As an application we determine the mean and
almost-sure lea...
D. A. Croydon, B. M. Hambly
Potential Analysis 29 (2008), no. 4, 351-389      2008年   [査読有り]
In this article, local limit theorems for sequences of simple random walks on
graphs are established. The results formulated are motivated by a variety of
random graph models, and explanations are provided as to how they apply to
supercritical per...
David A. Croydon
Journal of Statistical Physics 136 (2009), no. 2, 349-372      2009年   [査読有り]
We study the random walk Tex on the range of a simple random walk on
Tex in dimensions Tex. When Tex we establish quenched
and annealed scaling limits for the process Tex, which show that the
intersections of the original si...
David A. Croydon
Proceedings of the London Mathematical Society 94 (2007), no. 3, 672-694      2007年   [査読有り]
In this article, we consider the problem of estimating the heat kernel on
measure-metric spaces equipped with a resistance form. Such spaces admit a
corresponding resistance metric that reflects the conductivity properties of
the set. In this situ...
David A. Croydon
Adv. in Appl. Probab. Volume 39, Number 3 (2007), 708-730      2007年   [査読有り]
In this article a collection of random self-similar fractal dendrites is
constructed, and their Hausdorff dimension is calculated. Previous results
determining this quantity for random self-similar structures have relied on
geometrical properties ...
David A. Croydon
Publications of the Research Institute for Mathematical Sciences 48 (2012), no. 2, 279-338      2012年10月   [査読有り]
A scaling limit for the simple random walk on the largest connected component
of the Erdos-Renyi random graph in the critical window is deduced. The limiting
diffusion is constructed using resistance form techniques, and is shown to
satisfy the sa...
David A. Croydon
Advances in Applied Probability 42 (2010), no. 2, 528-558      2010年   [査読有り]
Consider a family of random ordered graph trees Tex, where
Tex has Tex vertices. It has previously been established that if the
associated search-depth processes converge to the normalised Brownian excursion
when rescaled appropria...
David Croydon
Probab. Theory Related Fields   157(3) 515-534   2013年   [査読有り]
In this article, a localisation result is proved for the biased random walk
on the range of a simple random walk in high dimensions (d \geq 5). This
demonstrates that, unlike in the supercritical percolation setting, a slowdown
effect occurs as so...
David A. Croydon
Annals of Probability 2009, Vol. 37, No. 3, 946-978      2009年   [査読有り]
A Brownian spatial tree is defined to be a pair Tex, where
Tex is the rooted real tree naturally associated with a Brownian
excursion and Tex is a random continuous function from Tex into
Tex such...
David Croydon
Ann. Inst. H. Poincare Probab. Statist. 44 (2008), no. 6, 987-1019      2008年   [査読有り]
In this article it is shown that the Brownian motion on the continuum random
tree is the scaling limit of the simple random walks on any family of discrete
Tex-vertex ordered graph trees whose search-depth functions converge to the
Brownian excurs...
David Croydon
Probability Theory and Related Fields 140 (2008), no. 1-2, 207-238      2006年12月   [査読有り]
In this article, we prove global and local (point-wise) volume and heat
kernel bounds for the continuum random tree. We demonstrate that there are
almost-surely logarithmic global fluctuations and log-logarithmic local
fluctuations in the volume o...