Symmetrized Random Permutations
- Creators
- Baik, Jinho
- Rains, Eric M.
- Others:
- Bleher, Pavel
- Its, Alexander
Abstract
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.
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.Attached Files
Published - baik.pdf
Submitted - 9910019.pdf
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Additional details
- Eprint ID
- 81862
- Resolver ID
- CaltechAUTHORS:20170926-160331200
- Created
-
2017-09-26Created from EPrint's datestamp field
- Updated
-
2023-06-02Created from EPrint's last_modified field
- Series Name
- Mathematical Sciences Research Institute publications
- Series Volume or Issue Number
- 40