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Symmetrized Random Permutations

Baik, Jinho and Rains, Eric M. (2001) Symmetrized Random Permutations. In: Random Matrix Models and Their Applications. Mathematical Sciences Research Institute publications . No.40. Cambridge University Press , Cambridge, pp. 1-19. ISBN 9780521802093.

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Selecting N random points in a unit square corresponds to selecting a random permutation. By putting 5 types of symmetry restrictions on the points, we obtain subsets of permutations : involutions, signed permutations and signed involutions. We are interested in the statistics of the length of the longest up/right path of random points selections in each symmetry type as the number of points increases to infinity. The limiting distribution functions are expressed in terms of Painlevé II equation. Some of them are Tracy-Widom distributions in random matrix theory, while there are two new classes of distribution functions interpolating GOE and GSE, and GUE and GOE^2 Tracy-Widom distribution functions. Also some applications and related topics are discussed.

Item Type:Book Section
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Additional Information:© 2001 Mathematical Sciences Research Institute. The authors thank the organizers of the workshop on Random Matrix Models and their Applications for their invitations.
Series Name:Mathematical Sciences Research Institute publications
Issue or Number:40
Record Number:CaltechAUTHORS:20170926-160331200
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81862
Deposited By: Tony Diaz
Deposited On:26 Sep 2017 23:13
Last Modified:03 Oct 2019 18:48

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