A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux
Copyright policy )A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux
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.
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
- New York University United States
- College of New Jersey United States
- Department of Mathematics Princeton University United States
- AT&T United States
- Institute for Advanced Study United States
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), Combinatorial probability, Nonlinear Sciences - Exactly Solvable and Integrable Systems, random permutation, Probability (math.PR), Plancherel measure, FOS: Physical sciences, Toeplitz determinant, Moment problems and interpolation problems in the complex plane, 004, 510, Moment problems, FOS: Mathematics, Mathematics - Combinatorics, Young diagram, Combinatorics (math.CO), Exactly Solvable and Integrable Systems (nlin.SI), Mathematics - Probability, Fredholm determinants
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), Combinatorial probability, Nonlinear Sciences - Exactly Solvable and Integrable Systems, random permutation, Probability (math.PR), Plancherel measure, FOS: Physical sciences, Toeplitz determinant, Moment problems and interpolation problems in the complex plane, 004, 510, Moment problems, FOS: Mathematics, Mathematics - Combinatorics, Young diagram, Combinatorics (math.CO), Exactly Solvable and Integrable Systems (nlin.SI), Mathematics - Probability, Fredholm determinants
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