Claeys, Tom
[UCL]
Its, A.
Krasovsky, I.
We study Fredholm determinants related to a family of kernels that describe the edge eigenvalue behavior in unitary random matrix models with critical edge points. The kernels are natural higher-order analogues of the Airy kernel and are built out of functions associated with the Painleve I hierarchy. The Fredholm determinants related to those kernels are higher-order generalizations of the Tracy-Widom distribution. We give an explicit expression for the determinants in terms of a distinguished smooth solution to the Painleve II hierarchy. In addition, we compute large gap asymptotics for the Fredholm determinants. (c) 2009 Wiley Periodicals, Inc.
Bibliographic reference |
Claeys, Tom ; Its, A. ; Krasovsky, I.. Higher-Order Analogues of the Tracy-Widom Distribution and the Painleve II Hierarchy. In: Communications on pure and applied mathematics, Vol. 63, no. 3, p. 362-412 (2010) |
Permanent URL |
http://hdl.handle.net/2078.1/73374 |