A PDE for the joint distributions of the Airy Process

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

In this paper, we answer a question posed by Kurt Johansson, to find a PDE for the joint distribution of the Airy Process. The latter is a continuous stationary process, describing the motion of the outermost particle of the Dyson Brownian motion, when the number of particles get large, with space and time appropriately rescaled. The question reduces to an asymptotic analysis on the equation governing the joint probability of the eigenvalues of coupled Gaussian Hermitian matrices. The differential equations lead to the asymptotic behavior of the joint distribution and the correlation for the Airy process at different times t_1 and t_2, when t_2-t_1 tends to infinity.
9 pages

Keywords

Probability, Mathematical Physics

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/66636

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0302329
 http://arxiv.org/abs/math/0302329

Collections

arXiv