Asymptotics of q-plancherel measures

• 成果类型: Article
• 署名作者: Feray, Valentin; Meliot, Pierre-Loic
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux; Universite Gustave-Eiffel
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-010-0331-6
• 发表日期: 2012
• 页码: 589-624
• 关键词: random young tableaux; symmetric-groups; random permutations; characters; diagrams; length

摘要

In this paper, we are interested in the asymptotic size of the rows and columns of a random Young diagram under a natural deformation of the Plancherel measure coming from Hecke algebras. The first lines of such diagrams are typically of order n, so it does not fit in the context of the work of Biane (Int Math Res Notices 4:179-192, 2001) and Aeniady (Probab. Theory Relat Fields 136:263-297, 2006). Using the theory of polynomial functions on Young diagrams of Kerov and Olshanski, we are able to compute explicitly the first- and second-order asymptotics of the length of the first rows. Our method also works for other measures, for example those coming from Schur-Weyl representations.