Random Words, Toeplitz Determinants and Integrable Systems. II
Exactly Solvable and Integrable Systems
2009-07-10 v2 Combinatorics
Abstract
This paper, a continuation of math.CO/9909169, connects the analysis of the length of the longest weakly increasing subsequence of inhomogeneous random words to a Riemann-Hilbert problem and an associated system of integrable PDEs. In particular, we show that the Poissonization of the distribution function of this length can be identified as the Jimbo-Miwa-Ueno tau function.
Cite
@article{arxiv.nlin/0004018,
title = {Random Words, Toeplitz Determinants and Integrable Systems. II},
author = {Alexander R. Its and Craig A. Tracy and Harold Widom},
journal= {arXiv preprint arXiv:nlin/0004018},
year = {2009}
}
Comments
The revised version corrects some misprints and adds some additional remarks