Asymptotics for the Covariance of the Airy_2 process
Abstract
In this paper we compute some of the higher order terms in the large-t asymptotic expansion of the Airy process two-point function, extending the previous work of Adler and van Moerbeke and Widom. We prove that it is possible to represent any order asymptotic approximation as a polynomial and integrals of the Hastings-McLeod Painlev\'e II function and its first derivative. Further, for up to tenth order we give this asymptotic approximation as a linear combination of the Tracy-Widom GUE density function f_2 and its derivatives. As a corollary to this, the asymptotic covariance is expressed up to tenth order in terms of the moments of the Tracy-Widom GUE distribution.
Keywords
Cite
@article{arxiv.1011.6616,
title = {Asymptotics for the Covariance of the Airy_2 process},
author = {Gregory Shinault and Craig A. Tracy},
journal= {arXiv preprint arXiv:1011.6616},
year = {2011}
}
Comments
14 pages. Version 2 adds some clarifying remarks and updates the references