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.
Communications in Mathematical Physics
- Pub Date:
- Mathematics - Combinatorics;
- Mathematics - Probability;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- 45 pages, ALX-LaTex, 9 figures, Lemma 2 (ii) is changed, |n|->