Probabilistic Weyl Law for Twisted Toeplitz Matrices with Rough Symbols

Abstract

In this article, we study the convergence of the empirical spectral measure of twisted Toeplitz matrices subject to small random perturbations. We show that the empirical spectral measure converges weakly in probability to the push-forward of the Lebesgue measure by the symbol. The symbol of the twisted Toeplitz matrices is assumed to be smooth in frequency, and only piecewise H{\"o}lder continuous with respect to the position variable with discontinuities of jump type.