Publications of the Research Institute for Mathematical Sciences

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Volume 47, Issue 1, 2011, pp. 361–374
DOI: 10.2977/PRIMS/38

Published online: 2011-03-24

Painlevé Functions in Statistical Physics

Craig A. Tracy[1] and Harold Widom[2]

(1) University of California at Davis, USA
(2) 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.

Keywords: Painlevé function, ASEP, Bethe Ansatz, KPZ scaling

Tracy Craig, Widom Harold: Painlevé Functions in Statistical Physics. Publ. Res. Inst. Math. Sci. 47 (2011), 361-374. doi: 10.2977/PRIMS/38