Painlev\'e Functions in Statistical Physics
Craig A. Tracy, Harold Widom
TL;DR
This paper reviews recent advances in the asymptotic behavior of the ASEP model in statistical physics, highlighting the role of Painlevé II functions in describing its limit laws and surveying their broader applications.
Contribution
It provides a comprehensive review of how Painlevé functions, especially Painlevé II, are used to describe limit laws in ASEP and discusses their significance in statistical physics.
Findings
Limit laws for ASEP are expressed via Painlevé II functions.
Painlevé functions appear in various statistical physics models.
The paper surveys the role of Painlevé functions beyond ASEP.
Abstract
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.
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