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A limit theorem for shifted Schur measures

By Craig A. Tracy and Harold Widom


To each partition λ = (λ1, λ2,...) with distinct parts we assign the probability Qλ(x)Pλ(y)/Z, where Qλ and Pλ are the Schur Q-functions and Z is a normalization constant. This measure, which we call the shifted Schur measure, is analogous to the much-studied Schur measure. For the specialization of the first m coordinates of x and the first n coordinates of y equal to α (0 < α < 1) and the rest equal to zero, we derive a limit law for λ1 as m, n → ∞ with τ = m/n fixed. For the Schur measure, the α-specialization limit law was derived by Johansson [J1]. Our main result implie

Year: 2004
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