Year: 2026
Type: preprint
Abstract: Consider the circular beta-ensembles, Jiang and Matsumoto computed the moments of traces, and proved central limit theorems for polynomial linear statistics using Jack functions. We give a direct proof of the Gaussian limits for the traces of powers of circular beta-ensembles using the theory of orthogonal polynomials on the unit circle and Stein's method. The proof relies on an explicit coupling of the Verblunsky coefficients of circular beta-ensembles, which also allow us to obtain almost sure and $L^2$ convergence.
Source: arXiv (Cornell University)
Author: Li, Yun
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7216014394