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.
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Received: 19 December 2000 / Accepted: 23 July 2001
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Baik, J., Deift, P. & Rains, E. A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux. Commun. Math. Phys. 223, 627–672 (2001). https://doi.org/10.1007/s002200100555
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DOI: https://doi.org/10.1007/s002200100555