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

Research output: Working paper

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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.