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Local statistics of Muttalib-Borodin ensemble in the hard to soft transitive regime and the related integrability
Local statistics of Muttalib-Borodin ensemble in the hard to soft transitive regime and the related integrability
Organizers
Speaker
Dong Wang
Time
Friday, March 28, 2025 1:00 PM - 2:30 PM
Venue
A3-4-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
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.