Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem

@inproceedings{Aldous1999LongestIS,
  title={Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem},
  author={David Aldous and Persi Diaconis},
  year={1999}
}
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 Baik-Deift-Johansson which yields limiting probability laws via hard analysis of Toeplitz determinants. 

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