On the Distribution of the Length of the Longest Increasing Subsequence of Random Permutations

Preprint
Publisher Website
Google Scholar
  • 16 October 1998
Abstract
Given uniform probability on the symmetric group of permutations of N elements, we consider the statistics of the longest increasing subsequence as N gets large. Limiting distribution (after centering and scaling) is obtained in terms of a solution of Painleve II equation, which shows that for large N, the longest increasing subsequence behaves statistically like the largest eigenvalue of a random GUE matrix. Also we obtained the asymptotics of the variance and the second leading term of the expectation.

This publication has 0 references indexed in Scilit: