Increasing subsequences and the hard-to-soft edge transition in matrix ensembles
Authors: Borodin A.1; Forrester P.J.2
Source: Journal of Physics A: Mathematical and General, Volume 36, Number 12, 2003 , pp. 2963-2981(19)
Publisher: Institute of Physics Publishing
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Abstract:
Our interest is in the cumulative probabilities Pr(L(t) l)for the maximum length of increasing subsequences in Poissonized ensembles of random permutations, random fixed point free involutions and reversed random fixed point free involutions. It is shown that these probabilities are equal to the hard edge gap probability for matrix ensembles with unitary, orthogonal and symplectic symmetry respectively. The gap probabilities can be written as a sum over correlations for certain determinantal point processes. From these expressions a proof can be given that the limiting form of Pr(L(t) l) in the three cases is equal to the soft edge gap probability for matrix ensembles with unitary, orthogonal and symplectic symmetry respectively, thereby reclaiming theorems due to Baik-Deift-Johansson and Baik-Rains.
Language: English
Document Type: Miscellaneous
Affiliations: 1: School of Mathematics, Institute of Advanced Study, Einstein Drive, Princeton, NJ 08540, USA 2: Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
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