Painlevé Functions in Statistical Physics

  • Craig A. Tracy

    University of California at Davis, USA
  • Harold Widom

    University of California at Santa Cruz, USA


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.

Cite this article

Craig A. Tracy, Harold Widom, Painlevé Functions in Statistical Physics. Publ. Res. Inst. Math. Sci. 47 (2011), no. 1, pp. 361–374

DOI 10.2977/PRIMS/38