Multilevel Dyson Brownian motions via Jack polynomials
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440_2014_Article_596.pdf
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Author(s)
Gorin, Vadim
Shkolnikov, Mykhaylo
Date Issued
November 2014
Journal
Probability Theory and Related Fields
Publisher
Springer-Verlag
Citation
Vadim, Gorin, and Mykhaylo Shkolnikov. "Multilevel Dyson Brownian motions via Jack polynomials" Probability Theory and Related Fields, vol. 163, no. 3, November 2014, pp. 413-463.
Version
Author's final manuscript
Abstract
We introduce multilevel versions of Dyson Brownian motions of arbitrary parameter β>0, generalizing the interlacing reflected Brownian motions of Warren for β=2. Such processes unify β 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 β≥1) and to give the corresponding link explicitly.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00440-014-0596-2
