相关论文: Probabilistic Weyl Law for Twisted Toeplitz Matric…
We study the behavior of the empirical distribution function of iterates of intermittent maps in the Hilbert space of square inegrable functions with respect to Lebesgue measure. In the long-range dependent case, we prove that the empirical…
We prove that if a rectangular matrix with uniformly small entries and approximately orthogonal rows is applied to the independent standardized random variables with uniformly bounded third moments, then the empirical CDF of the resulting…
We investigate the limit behaviour of the spectral measures of matrices following the Gibbs measure for the Ising model on random graphs, Potts model on random graphs, matrices coupled in a chain model or induced QCD model. For most of…
We study the asymptotic behavior of the appropriately scaled and possibly perturbed spectral measure $\mu$ of large random real symmetric matrices with heavy tailed entries. Specifically, consider the N by N symmetric matrix $Y_N^\sigma$…
In this article we consider the approximate description of doubly--dispersive channels by its symbol. We focus on channel operators with compactly supported spreading, which are widely used to represent fast fading multipath communication…
An EPR experiment is studied where each particle within the entangled pair undergoes a few weak measurements (WMs) along some pre-set spin orientations, with the outcomes individually recorded. Then the particle undergoes one strong…
A powerful tool for analyzing and approximating the singular values and eigenvalues of structured matrices is the theory of GLT sequences. By the GLT theory one can derive a function, which describes the singular value or the eigenvalue…
The precise measurement of parity-violating asymmetries in parity-violating electron scattering experiments is a powerful tool for probing new physics beyond the Standard Model. Achieving the expected precision requires both experimental…
This is a partly expository article for the volume "Algebraic and Analytic Microlocal Analysis" on pointwise Weyl laws for spectral projections kernels in the Kaehler setting. We prove a 2-term pointwise Weyl law for projections onto sums…
Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…
We show that the convolution of a compactly supported measure on $\mathbb{R}$ with a Gaussian measure satisfies a logarithmic Sobolev inequality (LSI). We use this result to give a new proof of a classical result in random matrix theory…
We study the asymptotic eigenvalue distribution of Toeplitz matrices generated by a singular symbol. It has been conjectured by Widom that, for a generic symbol, the eigenvalues converge to the image of the symbol. In this paper we ask how…
Inversion of Toeplitz matrices with singular symbol. Minimal eigenvalues. Three results are stated in this paper. The first one is devoted to the study of the orthogonal polynomial with respect of the weight $\varphi_{\alpha} (\theta)=\vert…
We study n by n symmetric random matrices H, possibly discrete, with iid above-diagonal entries. We show that H is singular with probability at most exp(-n^c), and the spectral norm of the inverse of H is O(sqrt{n}). Furthermore, the…
Elastic scattering of a twisted (Bessel) electron beam by CO$_2$ molecules is studied theoretically at high energies. The molecule's structure is optimized using coupled cluster theory and density functional theory with…
We consider the convergence of the empirical spectral measures of random $N \times N$ unitary matrices. We give upper and lower bounds showing that the Kolmogorov distance between the spectral measure and the uniform measure on the unit…
This paper studies the \(k^{th}-\)order slant Toeplitz and slant little Hankel operators on the weighted Bergman space \(\mathcal{A}_\alpha^2(\mathbb{D})\). These operators are constructed using a slant shift operator \(W_k\) composed with…
Bayesian inference with empirical likelihood faces a challenge as the posterior domain is a proper subset of the original parameter space due to the convex hull constraint. We propose a regularized exponentially tilted empirical likelihood…
In the literature, quite a few measures have been proposed for quantifying the deviation of a probability distribution from symmetry. The most popular of these skewness measures are based on the third centralized moment and on quantiles.…
The paper estimates the rate of convergence of the weak Euler approximation for the solutions of SDEs with Hoelder continuous coefficients driven by point and martingale measures. The equation considered has a non-degenerate main part whose…