Random Unitary Matrices, Permutations and Painleve

Details Random Unitary Matrices, Permutations and Painleve Random Unitary Matrices, Permutations and Painleve

1998-11-25

arxiv.org/abs/math/9811154v2

Commun. Math. Phys. 207 (1999), 665-685

Mathematics

Combinatorics

21 pages, 1 figure. Revised paper simplifies the statement of Theorem 1 and adds some additional references

Scientific paper

10.1007/s002200050741

This paper is concerned with certain connections between the ensemble of n x n unitary matrices -- specifically the characteristic function of the random variable tr(U) -- and combinatorics -- specifically Ulam's problem concerning the distribution of the length of the longest increasing subsequence in permutation groups -- and the appearance of Painleve functions in the answers to apparently unrelated questions. Among the results is a representation in terms of a Painleve V function for the characteristic function of tr(U) and (using recent results of Baik, Deift and Johansson) an expression in terms of a Painleve II function for the limiting distribution of the length of the longest increasing subsequence in the hyperoctahedral group.

Affiliated with

Also associated with

No associations

Rating

Random Unitary Matrices, Permutations and Painleve does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Random Unitary Matrices, Permutations and Painleve, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random Unitary Matrices, Permutations and Painleve will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-459119