2018年
Free probability for purely discrete eigenvalues of random matrices
Journal of the Mathematical Society of Japan
- ,
- ,
- 巻
- 70
- 号
- 3
- 開始ページ
- 1111
- 終了ページ
- 1150
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.2969/JMSJ/77147714
- 出版者・発行元
- MATH SOC JAPAN
In this paper, we study random matrix models which are obtained as a non-commutative polynomial in random matrix variables of two kinds: (a) a first kind which have a discrete spectrum in the limit, (b) a second kind which have a joint limiting distribution in Voiculescu's sense and are globally rotationally invariant. We assume that each monomial constituting this polynomial contains at least one variable of type (a), and show that this random matrix model has a set of eigenvalues that almost surely converges to a deterministic set of numbers that is either finite or accumulating to only zero in the large dimension limit. For this purpose we define a framework (cyclic monotone independence) for analyzing discrete spectra and develop the moment method for the eigenvalues of compact (and in particular Schatten class) operators. We give several explicit calculations of discrete eigenvalues of our model.
- リンク情報
-
- DOI
- https://doi.org/10.2969/JMSJ/77147714
- arXiv
- http://arxiv.org/abs/arXiv:1512.08975
- Web of Science
- https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000441857200013&DestApp=WOS_CPL
- URL
- https://publons.com/publon/21323122/
- ID情報
-
- DOI : 10.2969/JMSJ/77147714
- ISSN : 0025-5645
- ORCIDのPut Code : 59565659
- arXiv ID : arXiv:1512.08975
- Web of Science ID : WOS:000441857200013