2002/10/31 by Craig A. Tracy, Harold Widom · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.CO #math.PR #msc:60C05 #msc:60F05
paper · pdf · doi:10.1215/s0012-7094-04-12316-4
published as Duke Mathematical Journal 123 (2004), 171-208. · 35 pages, 2 figures. Version 3 adds a section on the Poisson limit of the shifted Schur measure
arxiv created 2003/07/21 · openalex publication_date 2004/05/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 implies that the two limit laws are identical.