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August 2020 High-dimensional limits of eigenvalue distributions for general Wishart process
Jian Song, Jianfeng Yao, Wangjun Yuan
Ann. Appl. Probab. 30(4): 1642-1668 (August 2020). DOI: 10.1214/19-AAP1539

Abstract

In this article, we obtain an equation for the high-dimensional limit measure of eigenvalues of generalized Wishart processes, and the results are extended to random particle systems that generalize SDEs of eigenvalues. We also introduce a new set of conditions on the coefficient matrices for the existence and uniqueness of a strong solution for the SDEs of eigenvalues. The equation of the limit measure is further discussed assuming self-similarity on the eigenvalues.

Citation

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Jian Song. Jianfeng Yao. Wangjun Yuan. "High-dimensional limits of eigenvalue distributions for general Wishart process." Ann. Appl. Probab. 30 (4) 1642 - 1668, August 2020. https://doi.org/10.1214/19-AAP1539

Information

Received: 1 January 2019; Revised: 1 September 2019; Published: August 2020
First available in Project Euclid: 4 August 2020

MathSciNet: MR4132637
Digital Object Identifier: 10.1214/19-AAP1539

Subjects:
Primary: 60F05 , 60H15

Keywords: Dyson Brownian motion , eigenvalue distribution , generalized Wishart process , high-dimensional limit , squared Bessel particle system , Wishart process

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 4 • August 2020
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