Random Words, Toeplitz Determinants and Integrable Systems. I

1999/09/28 by Alexander R. Its, Craig A. Tracy, Harold Widom
Mathematics · Physics and Astronomy · #math.CO #math-ph #math.MP #nlin.SI #solv-int

paper · pdf

published as Random Matrices and their Applications, eds. P. Bleher and A. Its, Cambridge University Press, New York, 2001, pgs. 245-258. · 15 pages, no figures

arxiv created 1999/09/28 · arxiv updated 2009/11/30

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.

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