JournalsprimsVol. 47, No. 1pp. 361–374

Painlevé Functions in Statistical Physics

  • Craig A. Tracy

    University of California at Davis, USA
  • Harold Widom

    University of California at Santa Cruz, USA
Painlevé Functions in Statistical Physics cover
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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 Painlevé II function. Furthermore, we take this opportunity to give a brief survey of the appearance of Painlevé functions in statistical physics.

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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