Operator level limit of the circular Jacobi $\beta$ensemble
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.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 DOI:
 10.48550/arXiv.2108.11039
 arXiv:
 arXiv:2108.11039
 Bibcode:
 2021arXiv210811039L
 Keywords:

 Mathematics  Probability
 EPrint:
 40 pages, no figures