Interacting Brownian motions in infinite dimensions related to the origin of the spectrum of random matrices
Volume 9, Issue 1 (2022), pp. 89–122
Pub. online: 10 January 2022
Type: Research Article
Open Access
Open Access
Received
11 August 2021
11 August 2021
Revised
8 November 2021
8 November 2021
Accepted
8 November 2021
8 November 2021
Published
10 January 2022
10 January 2022
Abstract
The generalised sine random point field arises from the scaling limit at the origin of the eigenvalues of the generalised Gaussian ensembles. We solve an infinite-dimensional stochastic differential equation (ISDE) describing an infinite number of interacting Brownian particles which is reversible with respect to the generalised sine random point field. Moreover, finite particle approximation of the ISDE is shown, that is, a solution to the ISDE is approximated by solutions to finite-dimensional SDEs describing finite-particle systems related to the generalised Gaussian ensembles.
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