Intertwinings of beta-Dyson Brownian motions of different dimensions
Kavita Ramanan, Mykhaylo Shkolnikov
TL;DR
This paper establishes a mathematical connection between beta-Dyson Brownian motions of different dimensions using Jack symmetric polynomials, removing previous technical restrictions and extending results to Ornstein-Uhlenbeck processes.
Contribution
It introduces a new proof linking beta-Dyson Brownian motions across dimensions without approximations, broadening the theoretical understanding of these processes.
Findings
Intertwining relations for all positive beta
Connection to Jack symmetric polynomials
Extension to Ornstein-Uhlenbeck processes
Abstract
We show that for all positive beta the semigroups of beta-Dyson Brownian motions of different dimensions are intertwined. The proof relates beta-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 beta>1 in [GS]. The corresponding results for beta-Dyson Ornstein-Uhlenbeck processes are also presented.
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