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Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem. (English) Zbl 0937.60001
Summary: We describe a simple one-person card game, patience sorting. Its analysis leads to a broad circle of ideas linking Young tableaux with the longest increasing subsequence of a random permutation via the Schensted correspondence. A recent highlight of this area is the work of J. Baik, P. A. Deift and K. Johansson [J. Am. Math. Soc. 12, No. 4, 1119-1178 (1999; Zbl 0932.05001)] which yields limiting probability laws via hard analysis of Toeplitz determinants.

##### MSC:
 60C05 Combinatorial probability 05E10 Combinatorial aspects of representation theory 15B52 Random matrices (algebraic aspects) 60F05 Central limit and other weak theorems 82C22 Interacting particle systems in time-dependent statistical mechanics 60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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