Random Words, Toeplitz Determinants and Integrable Systems. I
classification
🧮 math.CO
math-phmath.MPnlin.SIsolv-int
keywords
distributioneigenvaluesrandomcertainconstraintdeterminantsdirectensembles
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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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