Related papers: Wegner estimate for random divergence-type operato…
In this brief paper, we present a simple approach to estimate the variance of measurement noise with time-varying 1-D signals. The proposed approach exploits the relationship between the noise variance and the variance of the prediction…
Two proofs of a weighted weak-type $\left(1,\ldots,1;\frac{1}{m}\right)$ estimate for multilinear Calder\'on-Zygmund operators are given. The ideas are motivated by different proofs of the classical weak-type $(1,1)$ estimate for…
We apply weighted Mourre commutator theory to prove the limiting absorption principle for the discrete Schr{\"o}dinger operator perturbed by the sum of a Wigner-von Neumann and long-range type potential. In particular, this implies a new…
In this paper we prove the convergence of the eigenvalues of a random matrix that approximates a random Schr\"{o}dinger operator. Originally, such random operator arises from a stochastic heat equation. The proof uses a detailed topological…
We study an abstract class of autonomous differential inclusions in Hilbert spaces and show the well-posedness and causality, by establishing the operators involved as maximal monotone operators in time and space. Then the proof of the…
We prove normal typicality and dynamical typicality for a (centered) random block-band matrix model with block-dependent variances. A key feature of our model is that we achieve intermediate equilibration times, an aspect that has not been…
We prove a unique continuation principle for spectral projections of Schr\" odinger operators. We consider a Schr\" odinger operator $H= -\Delta + V$ on $\mathrm{L}^2(\mathbb{R}^d)$, and let $H_{\Lambda}$ denote its restriction to a finite…
We investigate the eigengenvalues problem for self-adjoint operators with the singular perturbations. The general results presented here includes weakly as well as strongly singular cases. We illustrate these results on two models which…
We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green…
In this paper, we consider the convergence rate with respect to the Wasserstein distance in the invariance principle for sequential dynamical systems. We utilize and modify the techniques previously employed for stationary sequences to…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
This paper provides estimates for the convergence rate of the total variation distance in the framework of the Breuer-Major theorem, assuming some smoothness properties of the underlying function. The results are proved by applying new…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
We refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed level, yet at this level (threshold) its coefficients can be…
In the proof of the invariance principle for locally perturbed periodic Lorentz process with finite horizon, a lot of delicate results were needed concerning the recurrence properties of its unperturbed version. These were analogous to the…
We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real line. Under minimal assumptions on the type of disorder, we…
We prove a simple uncertainty principle and show that it can be applied to prove Wegner estimates near fluctuation boundaries. This gives new classes of models for which localization at low energies can be proven.
Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. It is also a limiting property that results in many important non-monotonic averaging functions being excluded from the theoretical…
Operator monotone functions, introduced by Lowner in 1934, are an important class of real-valued functions. They arise naturally in matrix and operator theory and have various applications in other branches of mathematics and related…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…