We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
Tracy-Widom Distributions in Critical Unitary Random Matrix Ensembles and the Coupled Painlevé II System.
- Authors
Xu, Shuai-Xia; Dai, Dan
- Abstract
We study Fredholm determinants of the Painlevé II and Painlevé XXXIV kernels. In certain critical unitary random matrix ensembles, these determinants describe special gap probabilities of eigenvalues. We obtain Tracy-Widom formulas for the Fredholm determinants, which are explicitly given in terms of integrals involving a family of distinguished solutions to the coupled Painlevé II system in dimension four. Moreover, the large gap asymptotics for these Fredholm determinants are derived, where the constant terms are given explicitly in terms of the Riemann zeta-function.
- Subjects
FREDHOLM equations; PROBABILITY theory; EIGENVALUES; PAINLEVE equations; ZETA functions
- Publication
Communications in Mathematical Physics, 2019, Vol 365, Issue 2, p515
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-018-3257-y