On the distribution of the length of the second row of a Young diagram under Plancherel measure

Details On the distribution of the length of the second row of a Young diagram under Plancherel measure On the distribution of the length of the second row of a Young diagram under Plancherel measure

1999-01-26

arxiv.org/abs/math/9901118v1

Mathematics

Combinatorics

25 pages, AMS-LaTex file

Scientific paper

We investigate the probability distribution of the length of the second row of a Young diagram of size $N$ equipped with Plancherel measure. We obtain an expression for the generating function of the distribution in terms of a derivative of an associated Fredholm determinant, which can then be used to show that as $N\to\infty$ the distribution converges to the Tracy-Widom distribution [TW] for the second largest eigenvalue of a random GUE matrix. This paper is a sequel to [BDJ], where we showed that as $N\to\infty$ the distribution of the length of the first row of a Young diagram, or equivalently, the length of the longest increasing subsequence of a random permutation, converges to the Tracy-Widom distribution [TW] for the largest eigenvalue of a random GUE matrix.

Affiliated with

Also associated with

No associations

Rating

On the distribution of the length of the second row of a Young diagram under Plancherel measure 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 On the distribution of the length of the second row of a Young diagram under Plancherel measure, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the distribution of the length of the second row of a Young diagram under Plancherel measure will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-237440