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Painlev\'e Functions in Statistical Physics

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arxiv 0912.2362 v2 pith:U5VYZK2M submitted 2009-12-14 math.PR math-phmath.MPnlin.SI

Craig A. Tracy , Harold Widom This is my paper · ORCID
classification math.PRmath-phmath.MPnlin.SI
keywords painlevfunctionslawslimitphysicsstatisticalappearanceasep
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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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Cited by 1 Pith paper

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  1. Emptiness formation probability and Painlev\'e V equation in the XY spin chain

    cond-mat.stat-mech 2019-09 conditional novelty 6.0 of 10

    The emptiness formation probability of the XY chain, in the double-scaling limit near its critical lines, is governed by a Painleve V tau function; the result is exact at the Ising point and numerically supported elsewhere.

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