Painlevé Functions in Statistical Physics

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 Painlevé II function. Furthermore, we take this opportunity to give a brief survey of the appearance of Painlevé functions in statistical physics.

Revised version updates some references

References in corpus (8)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• The one-dimensional KPZ equation: an exact solution and its universality
• Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals
• Asymptotics in ASEP with Step Initial Condition
• Exact height distributions for the KPZ equation with narrow wedge initial condition
• A Fredholm Determinant Representation in ASEP
• The crossover regime for the weakly asymmetric simple exclusion process
• On the Numerical Evaluation of Distributions in Random Matrix Theory: A Review

Cited by in corpus (11)

• Conformal field theory of Painlevé VI
• Domain wall dynamics in the Landau--Lifshitz magnet and the classical-quantum correspondence for spin transport
• Convergence from Divergence
• Emptiness formation probability and Painlevé V equation in the XY spin chain
• On the Existence of Monodromies for the Rabi model
• Two-dimensional Yang-Mills theory, Painleve equations and the six-vertex model
• Galoisian Methods for Testing Irreducibility of Order Two Nonlinear Differential Equations
• Factorization of Ising correlations C(M,N) for $\nu =-k$ and M+N odd, $M\le N$, $T<T_c$ and their lambda extensions
• Connection problem of the first Painlevé transcendents with large initial data
• Perturbed Laguerre Unitary Ensembles, Painlevé V and Information Theory
• On the Question of the Bäcklund Transformations and Jordan Generalizations of the Second Painlevé Equation