Center of Mass distribution of the Jacobi unitary ensembles Painleve V, asympototic expansions

Blower, Gordon and Zhan, Longjun and Chen, Yang and Zhu, Mengkun (2017) Center of Mass distribution of the Jacobi unitary ensembles Painleve V, asympototic expansions. Working Paper. UNSPECIFIED. (Unpublished)

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Abstract

In this paper, we study the probability distribution of the center of mass of the finite n Jacobi unitary ensembles with parameters alpha and beta; that is the probability that trace M_n is in (c, c+dc), where M_n are n by n matrices of the Jacobi unitary ensemble. We first compute the eponential moment generating function of the linear statistics c=x_1+...+x_n.