Year: 2025
Type: article
Abstract: We study mesoscopic fluctuations of orthogonal polynomial ensembles on the unit circle. We show that asymptotics of such fluctuations are stable under decaying perturbations of the recurrence coefficients, where the appropriate decay rate depends on the scale considered. By directly proving Gaussian limits for certain constant coefficient ensembles, we obtain mesoscopic scale Gaussian limits for a large class of orthogonal polynomial ensembles on the unit circle. As a corollary we prove mesoscopic central limit theorems (for all mesoscopic scales) for the $$\beta =2$$ β = 2 circular Jacobi ensembles with real parameter $$\delta >-1/2$$ δ > - 1 / 2 .
Authors: Jonathan Breuer, Daniel Ofner
Institution: Hebrew University of Jerusalem
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
Awards: Institut Mittag-Leffler, G7124960189
OpenAlex ID: W4414786447