A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux
Combinatorics
2009-10-31 v4 Probability
Exactly Solvable and Integrable Systems
Abstract
We obtain an identity between Fredholm determinants of two kinds of operators, one acting on functions on the unit circle and the other acting on functions on a subset of the integers. This identity is a generalization of an identity between a Toeplitz determinant and a Fredholm determinant that has appeared in the random permutation context. Using this identity, we prove, in particular, convergence of moments for arbitrary rows of a random Young diagram under Plancherel measure.
Keywords
Cite
@article{arxiv.math/0012117,
title = {A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux},
author = {Jinho Baik and Percy Deift and Eric Rains},
journal= {arXiv preprint arXiv:math/0012117},
year = {2009}
}
Comments
45 pages, ALX-LaTex, 9 figures, Lemma 2 (ii) is changed, |n|->n in (2.7) and (2.8), new index system, Remark 2.3, 2.13 added