Matrix harmonic analysis at high temperature via the Dirichlet process

Fuente: arXiv
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Autore principale: Zhang, Jiyuan
Natura: Preprint
Pubblicazione: 2025
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author Zhang, Jiyuan
author_facet Zhang, Jiyuan
contents We investigate harmonic analysis of random matrices of large size with their Dyson indices going simultaneous to zero, that is in the high temperature limit. In this regime, we show that the multivariate Bessel function/Heckman-Opdam hypergeometric function of the empirical spectral distribution converges to the Fourier/Mellin transform of a measure, which and the limiting empirical distribution are intimately related by the Markov-Krein correspondence. The uniqueness, existence and other properties of the Markov-Krein correspondence can be studied using the theory of the Dirichlet process.
format Preprint
id arxiv_https___arxiv_org_abs_2508_21349
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Matrix harmonic analysis at high temperature via the Dirichlet process
Zhang, Jiyuan
Mathematical Physics
Probability
60F05, 60G57, 20C30, 60B20
We investigate harmonic analysis of random matrices of large size with their Dyson indices going simultaneous to zero, that is in the high temperature limit. In this regime, we show that the multivariate Bessel function/Heckman-Opdam hypergeometric function of the empirical spectral distribution converges to the Fourier/Mellin transform of a measure, which and the limiting empirical distribution are intimately related by the Markov-Krein correspondence. The uniqueness, existence and other properties of the Markov-Krein correspondence can be studied using the theory of the Dirichlet process.
title Matrix harmonic analysis at high temperature via the Dirichlet process
topic Mathematical Physics
Probability
60F05, 60G57, 20C30, 60B20
url https://arxiv.org/abs/2508.21349