A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux
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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2001
 DOI:
 10.1007/s002200100555
 arXiv:
 arXiv:math/0012117
 Bibcode:
 2001CMaPh.223..627B
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Probability;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 45 pages, ALXLaTex, 9 figures, Lemma 2 (ii) is changed, n>