Related papers: Wegner estimate and localization for alloy-type mo…
We study discrete alloy-type random Schr\"odinger operators on $\ell^2(\mathbb{Z}^d)$. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. If the…
We study Anderson and alloy type random Schr\"odinger operators on $\ell^2(\ZZ^d)$ and $L^2(\RR^d)$. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of…
We prove a Wegner estimate for alloy type models merely assuming that the single site potential is lower bounded by a characteristic function of a thick set, that is a particular set of positive measure. The proof is based on two…
We study Schroedinger operators with a random potential of alloy type. The single site potentials are allowed to change sign. For a certain class of them we prove a Wegner estimate. This is a key ingredient in an existence proof of pure…
We review recent and give some new results on the spectral properties of Schroedinger operators with a random potential of alloy type. Our point of interest is the so called Wegner estimate in the case where the single site potentials…
I consider random Schr\"odinger operators with exponentially decaying single site potential, which is allowed to change sign. For this model, I prove Anderson localization both in the sense of exponentially decaying eigenfunctions and…
We consider Schroedinger operators with a random potential of alloy type on infinite metric graphs which obey certain uniformity conditions. For single site potentials of fixed sign we prove that the random Schroedinger operator restricted…
We study spectral properties of ergodic random Schr\"odinger operators on $L^2 (\RR^d)$. The density of states is shown to exist for a certain class of alloy type potentials with single site potentials of changing sign. The Wegner estimate…
We study spectral properties of Schr\"odinger operators with random potentials of alloy type on $L^2(\RR)$ and their restrictions to finite intervals. A Wegner estimate for non-negative single site potentials with small support is proven.…
We consider an alloy type potential on an infinite metric graph. We assume a covering condition on the single site potentials. For random Schr\"odingers operator associated with the alloy type potential restricted to finite volume subgraphs…
We study spectra of alloy-type random Schr\"odinger operators on metric graphs. For finite edge subsets of general graphs we prove a Wegner estimate which is linear in the volume (i.e. the number of edges) and the length of the considered…
We extend methods of Ding and Smart from their breakthrough paper in 2020 which showed Anderson localization for certain random Schr\"odinger operators on $\ell^2(\mathbb{Z}^2)$ via a quantitative unique continuation principle and Wegner…
We review recent results on localization for discrete alloy-type models based on the multiscale analysis and the fractional moment method, respectively. The discrete alloy-type model is a family of Schr\"odinger operators $H_\omega = -…
We prove a Wegner estimate for discrete Schr\"odinger operators with a potential given by a Gaussian random process. The only assumption is that the covariance function decays exponentially, no monotonicity assumption is required. This…
We prove a conditional Wegner estimate for Schr\"odinger operators with random potentials of breather type. More precisely, we reduce the proof of the Wegner estimate to a scale free unique continuation principle. The relevance of such…
We study localization and derive stochastic estimates (in particular, Wegner and Minami estimates) for the eigenvalues of weakly correlated random discrete Schr\"odinger operators in the localized phase. We apply these results to obtain…
One of the fundamental results in the theory of localization for discrete Schr\"odinger operators with random potentials is the exponential decay of Green's function and the absence of continuous spectrum. In this paper we provide a new…
We consider a family of self-adjoint operators [H_\omega = - \Delta + \lambda V_\omega, \quad \omega \in \Omega = \bigtimes_{k \in \ZZ^d} \RR,] on the Hilbert space $\ell^2 (\ZZ^d)$ or $L^2 (\RR^d)$. Here $\Delta$ denotes the Laplace…
The present paper is devoted to the study of spectral properties of random Schroedinger operators. Using a finite section method for Toeplitz matrices, we prove a Wegner estimate for some alloy type models where the single site potential is…
We exhibit d-dimensional limit-periodic Schrodinger operators that are uniformly localized in the strongest sense possible. That is, for each of these operators, there is a uniform exponential decay rate such that every element of the hull…