Painlevé Functions in Statistical Physics

Details Painlevé Functions in Statistical Physics Painlevé Functions in Statistical Physics

2009-12-14

arxiv.org/abs/0912.2362v2

Publ. RIMS Kyoto Univ., 47 (2011), 361-374

Mathematics

Probability

Revised version updates some references

Scientific paper

10.2977/PRIMS/38

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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