Random Words, Toeplitz Determinants and Integrable Systems. I
Combinatorics
2007-05-23 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
solv-int
Abstract
It is proved that the limiting distribution of the length of the longest weakly increasing subsequence in an inhomogeneous random word is related to the distribution function for the eigenvalues of a certain direct sum of Gaussian unitary ensembles subject to an overall constraint that the eigenvalues lie in a hyperplane.
Cite
@article{arxiv.math/9909169,
title = {Random Words, Toeplitz Determinants and Integrable Systems. I},
author = {Alexander R. Its and Craig A. Tracy and Harold Widom},
journal= {arXiv preprint arXiv:math/9909169},
year = {2007}
}
Comments
15 pages, no figures