Related papers: Almost sure Weyl law for quantized tori

For the Toeplitz quantization of complex-valued functions on a $2n$-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law. In numerical…

We study the spectra of $N\times N$ Toeplitz band matrices perturbed by small complex Gaussian random matrices, in the regime $N\gg 1$. We prove a probabilistic Weyl law, which provides an precise asymptotic formula for the number of…

We study the spectra of general $N\times N$ Toeplitz matrices given by symbols in the Wiener Algebra perturbed by small complex Gaussian random matrices, in the regime $N\gg 1$. We prove an asymptotic formula for the number of eigenvalues…

This paper proves a probabilistic Weyl-law for the spectrum of randomly perturbed Berezin-Toeplitz operators, generalizing a result proven by Martin Vogel in 2020. This is done following Vogel's strategy using an exotic symbol calculus…

We consider quite general $h$-pseudodifferential operators on $R^n$ with small random perturbations and show that in the limit of small $h$ the eigenvalues are distributed according to a Weyl law with a probabality that tends to 1. The…

In this paper, we investigate the singular values of a natural family of transfer operators twisted by large random permutation matrices. In the large N limit, we obtain a Weyl law for its singular values, valid asymptotically almost surely…

In this work we consider semi-classical Schr\"odinger operators with potentials supported in a bounded strictly convex subset ${\cal O}$ of ${\bf R}^n$ with smooth boundary. Letting $h$ denote the semi-classical parameter, we consider…

In this paper, we consider elliptic differential operators on compact manifolds with a random perturbation in the 0th order term and show under fairly weak additional assumptions that the large eigenvalues almost surely distribute according…

We consider the eigenvalues of a fixed, non-normal matrix subject to a small additive perturbation. In particular, we consider the case when the fixed matrix is a banded Toeplitz matrix, where the bandwidth is allowed to grow slowly with…

We consider quite general differential operators on the circle with a small random lower order perturbation. We embrace two points a view, the semiclassical and the high energy limits. We show (a) in the semiclassical limit, that the…

We present some results concerning the almost sure behaviour of the operator norm or random Toeplitz matrices, including the law of large numbers for the norm, normalized by its expectation (in the i.i.d. case). As tools we present some…

We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criteria for a…

We give an asymptotic evaluation for the number of automorphic characters of an algebraic torus $T$ with bounded analytic conductor. The analytic conductor which we use is defined via the local Langlands correspondence for tori by choosing…

We consider an $N \times N$ random symmetric Toeplitz matrix with an i.i.d. input sequence drawn from a distribution that lies in the domain of attraction of an $\alpha$-stable law for $0 < \alpha < 2$. We show that under an appropriate…

We study the number of exponentially small singular values of the semiclassical $\overline{\partial}$ operator on exponentially weighted $L^2$ spaces on the two-dimensional torus. Accurate upper and lower bounds on the number of such…

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…

Let $T_N$ denote an $N\times N$ Toeplitz matrix with finite, $N$ independent symbol ${\bf a}$. For $E_N$ a noise matrix satisfying mild assumptions (ensuring, in particular, that $N^{-1/2}\|E_N\|_{{\rm HS}}\to_{N\to\infty} 0$ at a…

We study the distribution of eigenvalues for non-selfadjoint perturbations of selfadjoint semiclassical analytic pseudodifferential operators in dimension two, assuming that the classical flow of the unperturbed part is completely…

A Weyl law for Toeplitz operators was proved by Boutet de Monvel and Guillemin for general Toeplitz structures. In the setting of positive line bundles, we revisit this theme in light of local asymptotic techniques based on the microlocal…

In this paper we give an estimate on the asymptotic behavior of eigenvalues of discretized elliptic boundary values problems. We first prove a simple min-max principle for selfadjoint operators on a Hilbert space. Then we show two sided…