A DETERMINANTAL POINT PROCESS APPROACH TO SCALING AND LOCAL LIMITS OF RANDOM YOUNG TABLEAUX

• 成果类型: Article
• 署名作者: Borga, Jacopo; Boutillier, Cedric; Feray, Valentin; Meliot, Pierre-Loic
• 署名单位: Stanford University; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite de Lorraine; Universite Paris Saclay
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1706
• 发表日期: 2025
• 页码: 299-354
• 关键词: plancherel measures; symmetrical group; plane partitions; asymptotics; characters; shapes

摘要

We obtain scaling and local limit results for large random Young tableaux of fixed shape )0 via the asymptotic analysis of a determinantal point process due to Gorin and Rahman (2019). More precisely, we prove: - an explicit description of the limiting surface of a uniform random Young tableau of shape )0, based on solving a complex-valued polynomial equation, - a simple criteria to determine if the limiting surface is continuous in the whole domain, - and a local limit result in the bulk of a random Poissonized Young tableau of shape )0. Our results have several consequences, for instance: they lead to explicit formulas for the limiting surface of L-shaped tableaux, generalizing the results of Pittel and Romik (2007) for rectangular shapes; they imply that the limiting surface for L-shaped tableaux is discontinuous for almost-every Lshape, and they give a new one-parameter family of infinite random Young tableaux, constructed from the so-called random infinite bead process.