Random Permutations and Random Matrix
Jinho Baik
Mathematics Department
University of Michigan
Abstract
Consider a permutation, say 51324. The subsequence 124
is an increasing subsequence. The question of interest is if one
picks a permutation of size N at random, what is the typical
length of the longest increasing subsequence as N gets large ? It
turned out that this has something to do with eigenvalues of
random matrix, the area that is originated in nuclear physics in
1950's and then finds many applications in physics, statistics and
mathematics. We discuss this connection and also other related
problems like random tiling and random growth processes.