Operator level limit of the circular Jacobi $\beta$-ensemble

Yun Li; Benedek Valkó

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arXiv · 2108.11039

Operator level limit of the circular Jacobi $\beta$-ensemble

Yun Li·Benedek Valkó

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Abstract

We prove an operator level limit for the circular Jacobi $\beta$-ensemble. As a result, we characterize the counting function of the limit point process via coupled systems of stochastic differential equations. We also show that the normalized characteristic polynomials converge to a random analytic function, which we characterize via the joint distribution of its Taylor coefficients at zero and as the solution of a stochastic differential equation system. We also provide analogous results for the real orthogonal $\beta$-ensemble.

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Yun Li, Benedek Valkó. 2021-08-25. Operator level limit of the circular Jacobi $\beta$-ensemble. https://arxiv.org/abs/2108.11039

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