Painlevé functions in statistical physics
The authors give a brief survey on the appearance of Painlevé functions in statistical physics. The idea to write such a paper arose after studying the recent progress in limit laws for the one-dimensional asymmetric simple exclusion process (ASEP) on the integer lattice. The matter is that, under certain conditions [see \textit{A. Soshnikov}, ``Determinantal random fields,'' Russ. Math. Surv. 55, No.~5, 923--975 (2000); translation from Usp. Mat. Nauk 55, No. 5, 107--160 (2000; Zbl 0991.60038)], in such processes, correlation functions are expressible in terms of Painlevé functions.
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