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== Random partitions ==
There is a deep theory of random partitions chosen according to the uniform probability distribution on the [[symmetric group]] via the [[Robinson–Schensted correspondence]]. In 1977, Logan and Shepp, as well as Vershik and Kerov, showed that the Young diagram of a typical large partition becomes asymptotically close to the graph of a certain analytic function minimizing a certain functional. In 1988, Baik, Deift and Johansson extended these results to determine the distribution of the longest increasing subsequence of a random permutation in terms of the [[Tracy–Widom distribution]].<ref>{{Cite book |last=Romik |first=Dan |title=The surprising mathematics of longest increasing subsequences |date=2015 |publisher=Cambridge University Press |isbn=978-1-107-42882-9 |series=Institute of Mathematical Statistics Textbooks |___location=New York}}</ref> [[Andrei Okounkov|Okounkov]] related these results to the combinatorics of [[Riemann surface]]s and representation theory.<ref>{{Cite journal |last=Okounkov |first=Andrei |date=2000 |title=Random matrices and random permutations
== See also ==
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