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• W2137975592 abstract "We consider the distributions of the lengths of the longest weakly increasing and strongly decreasing subsequences in words of length N from an alphabet of k letters. We find Toeplitz determinant representations for the exponential generating functions (on N) of these distribution functions and show that they are expressible in terms of solutions of Painlev'e V equations. We show further that in the weakly increasing case the generating function gives the distribution of the smallest eigenvalue in the k x k Laguerre random matrix ensemble and that the distribution itself has, after centering and normalizing, an N -> infinity limit which is equal to the distribution function for the largest eigenvalue in the Gaussian Unitary Ensemble of k x k hermitian matrices of trace zero." @default.
• W2137975592 created "2016-06-24" @default.
• W2137975592 creator A5011123024 @default.
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• W2137975592 date "2001-03-01" @default.
• W2137975592 modified "2023-10-10" @default.
• W2137975592 title "On the distributions of the lengths of the longest monotone subsequences in random words" @default.
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• W2137975592 doi "https://doi.org/10.1007/pl00008763" @default.
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