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Local statistics of Muttalib-Borodin ensemble in the hard to soft transitive regime and the related integrability

组织者

赛蒙·阿尔塔莫诺夫 , 帕维尔·尼基丁 , 沙米尔·沙基洛夫

演讲者

Dong Wang

时间

2025年03月28日 13:00 至 14:30

地点

A3-4-301

线上

Zoom 242 742 6089 (BIMSA)

摘要

Muttalib-Borodin ensemble is a typical biorthogonal ensemble. It has a hard edge limit that is expressed by Wright's generalized Bessel functions, or by Meijer G functions if the parameter $\theta$ is an integer. This hard edge limit does not occur in orthogonal polynomial ensembles unless $\theta = 1$. In this talk we consider the transition from the hard edge limit to the soft edge limit of the Muttalib-Borodin ensemble with an integer $\theta$ parameter, and show that the limiting distributions are related to Painleve-type equations. Our result generalizes the known relation between the transitive regime of orthogonal polynomial ensemble and the Painleve XXXIV. This is joint work with Shui-Xia Xu.