2019/12/17 by Alberts, Tom, Normand, Raoul
#15B52 #60B20 #60F10 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1912.07788
We study the dimension properties of the spectral measure of the Circular β-Ensembles. For β≥ 2 it it was previously shown by Simon that the spectral measure is almost surely singular continuous with respect to Lebesgue measure on ∂ \mathbbD and the dimension of its support is 1 - 2/β. We reprove this result with a combination of probabilistic techniques and the so-called Jitomirskaya-Last inequalities. Our method is simpler in nature and mostly self-contained, with an emphasis on the probabilistic aspects rather than the analytic. We also extend the method to prove a large deviations principle for norms involved in the Jitomirskaya-Last analysis.