Intertwinings of beta-Dyson Brownian motions of different dimensions

Kavita Ramanan; Mykhaylo Shkolnikov

doi:10.1214/17-AIHP835

Intertwinings of beta-Dyson Brownian motions of different dimensions

Kavita Ramanan, Mykhaylo Shkolnikov

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3 Scopus citations

Abstract

We show that for all positive β the semigroups of β-Dyson Brownian motions of different dimensions are intertwined. The proof relates β-Dyson Brownian motions directly to Jack symmetric polynomials and omits an approximation of the former by discrete space Markov chains, thereby disposing of the technical assumption β ≥ 1 in (Probab. Theory Related Fields 163 (2015) 413–463). The corresponding results for β-Dyson Ornstein–Uhlenbeck processes are also presented.

Original language	English (US)
Pages (from-to)	1152-1163
Number of pages	12
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	54
Issue number	2
DOIs	https://doi.org/10.1214/17-AIHP835
State	Published - May 2018

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Dixon–Anderson conditional probability density
Dyson Brownian motions
Dyson Ornstein–Uhlenbeck processes
Gaussian random matrix ensembles
Intertwinings
Jack symmetric polynomials

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abstract = "We show that for all positive β the semigroups of β-Dyson Brownian motions of different dimensions are intertwined. The proof relates β-Dyson Brownian motions directly to Jack symmetric polynomials and omits an approximation of the former by discrete space Markov chains, thereby disposing of the technical assumption β ≥ 1 in (Probab. Theory Related Fields 163 (2015) 413–463). The corresponding results for β-Dyson Ornstein–Uhlenbeck processes are also presented.",

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doi = "10.1214/17-AIHP835",

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T1 - Intertwinings of beta-Dyson Brownian motions of different dimensions

AU - Ramanan, Kavita

AU - Shkolnikov, Mykhaylo

N1 - Publisher Copyright: © Association des Publications de l’Institut Henri Poincaré, 2018.

PY - 2018/5

Y1 - 2018/5

N2 - We show that for all positive β the semigroups of β-Dyson Brownian motions of different dimensions are intertwined. The proof relates β-Dyson Brownian motions directly to Jack symmetric polynomials and omits an approximation of the former by discrete space Markov chains, thereby disposing of the technical assumption β ≥ 1 in (Probab. Theory Related Fields 163 (2015) 413–463). The corresponding results for β-Dyson Ornstein–Uhlenbeck processes are also presented.

AB - We show that for all positive β the semigroups of β-Dyson Brownian motions of different dimensions are intertwined. The proof relates β-Dyson Brownian motions directly to Jack symmetric polynomials and omits an approximation of the former by discrete space Markov chains, thereby disposing of the technical assumption β ≥ 1 in (Probab. Theory Related Fields 163 (2015) 413–463). The corresponding results for β-Dyson Ornstein–Uhlenbeck processes are also presented.

KW - Dixon–Anderson conditional probability density

KW - Dyson Brownian motions

KW - Dyson Ornstein–Uhlenbeck processes

KW - Gaussian random matrix ensembles

KW - Intertwinings

KW - Jack symmetric polynomials

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JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

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ER -

Intertwinings of beta-Dyson Brownian motions of different dimensions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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