Random Words, Toeplitz Determinants and Integrable Systems. I

Details Random Words, Toeplitz Determinants and Integrable Systems. I Random Words, Toeplitz Determinants and Integrable Systems. I

1999-09-28

arxiv.org/abs/math/9909169v1

Random Matrices and their Applications, eds. P. Bleher and A. Its, Cambridge University Press, New York, 2001, pgs. 245-258.

Mathematics

Combinatorics

15 pages, no figures

Scientific paper

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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