2021/08/25 by Li, Yun, Valkó, Benedek
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2108.11039
We prove an operator level limit for the circular Jacobi β-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 β-ensemble.