Multilevel Dyson Brownian motions via Jack polynomials
成果类型：
Article
署名作者：
Gorin, Vadim; Shkolnikov, Mykhaylo
署名单位：
Massachusetts Institute of Technology (MIT); Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS; University of California System; University of California Berkeley
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-014-0596-2
发表日期：
2015
页码：
413-463
关键词：
摘要：
We introduce multilevel versions of Dyson Brownian motions of arbitrary parameter , generalizing the interlacing reflected Brownian motions of Warren for . Such processes unify corners processes and Dyson Brownian motions in a single object. Our approach is based on the approximation by certain multilevel discrete Markov chains of independent interest, which are defined by means of Jack symmetric polynomials. In particular, this approach allows to show that the levels in a multilevel Dyson Brownian motion are intertwined (at least for ) and to give the corresponding link explicitly.
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