Mathematical Research Letters

Volume 5 (1998)

Number 1

The longest increasing subsequence in a random permutation and a unitary random matrix model

Pages: 68 – 82

DOI: http://dx.doi.org/10.4310/MRL.1998.v5.n1.a6

Author

Kurt Johansson (Royal Institute of Technology)

Abstract

If $L_N$ is the expected length of the longest increasing subsequence in a random permutation, then $L_N\sim 2\sqrt{N}$ as $N\to\infty$. We give a new proof of this result using a connection with a certain unitary random matrix model. The asymptotic formula is directly related to a third order phase transition in this model found by Gross and Witten.

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