Mesoscopic Universality for Circular Orthogonal Polynomial Ensembles
Mesoscopic Universality for Circular Orthogonal Polynomial Ensembles
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 …