Painlevé functions in statistical physics
type: Item
instance of: scholarly article
title: Painlevé functions in statistical physics
zbMATH Open document ID: 1221.34240
DOI: 10.2977/PRIMS/38
author: Craig A. Tracy
author: Harold Widom
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2011-05-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/0912.2362
review text: The authors give a brief survey on the appearance of Painlevé functions in statistical physics. The idea to write such a paper arose after studying the recent progress in limit laws for the one-dimensional asymmetric simple exclusion process (ASEP) on the integer lattice. The matter is that, under certain conditions [see \textit{A. Soshnikov}, ``Determinantal random fields,'' Russ. Math. Surv. 55, No.~5, 923--975 (2000); translation from Usp. Mat. Nauk 55, No. 5, 107--160 (2000; Zbl 0991.60038)], in such processes, correlation functions are expressible in terms of Painlevé functions.
Mathematics Subject Classification ID: 34M55
Mathematics Subject Classification ID: 82B23
zbMATH DE Number: 5883098
zbMATH Keywords: Painlevé function
zbMATH Keywords: ASEP
zbMATH Keywords: Bethe ansatz
zbMATH Keywords: KPZ scaling
Wikidata QID: Q56950548
reviewed by: Mykola Grygorenko
MaRDI profile type: Publication
arXiv ID: 0912.2362
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description: scientific article