A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux
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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.
KeywordsUnit Circle Young Diagram Random Permutation Young Tableau Fredholm Determinant
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