Higher-order analogues of the Tracy-Widom distribution and the Painlevé II hierarchy
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Publication:3406734
DOI10.1002/CPA.20284zbMATH Open1198.34191arXiv0901.2473OpenAlexW2165337351MaRDI QIDQ3406734
Author name not available (Why is that?)
Publication date: 19 February 2010
Published in: (Search for Journal in Brave)
Abstract: We study Fredholm determinants related to a family of kernels which 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 Painlev'e 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 Painlev'e II hierarchy. In addition we compute large gap asymptotics for the Fredholm determinants.
Full work available at URL: https://arxiv.org/abs/0901.2473
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