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 e-prints
- Pub Date:
- August 2021
- DOI:
- 10.48550/arXiv.2108.11039
- arXiv:
- arXiv:2108.11039
- Bibcode:
- 2021arXiv210811039L
- Keywords:
-
- Mathematics - Probability
- E-Print:
- 40 pages, no figures