arXiv Analytics

Sign in

arXiv:0912.2362 [math.PR]AbstractReferencesReviewsResources

Painlevé Functions in Statistical Physics

Craig A. Tracy, Harold Widom

Published 2009-12-14, updated 2010-04-27Version 2

We review recent progress in limit laws for the one-dimensional asymmetric simple exclusion process (ASEP) on the integer lattice. The limit laws are expressed in terms of a certain Painlev\'e II function. Furthermore, we take this opportunity to give a brief survey of the appearance of Painlev\'e functions in statistical physics.

Comments: Revised version updates some references
Journal: Publ. RIMS Kyoto Univ., 47 (2011), 361-374
Categories: math.PR, math-ph, math.MP, nlin.SI
Subjects: 34M55, 60K35, 82B23
Related articles: Most relevant | Search more
arXiv:1712.04911 [math.PR] (Published 2017-12-13)
Statistical physics on a product of trees
arXiv:1205.4054 [math.PR] (Published 2012-05-17)
The Bose Gas and Asymmetric Simple Exclusion Process on the Half-Line
arXiv:2103.08019 [math.PR] (Published 2021-03-14)
Quasi-static limit for the asymmetric simple exclusion

Links

Toolbox