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

Details A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux

2000-12-14

arxiv.org/abs/math/0012117v4

Mathematics

Combinatorics

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

Scientific paper

10.1007/s002200100555

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.

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