Related papers: Density of States under non-local interactions II.…
Following [7,8], we analyze regularity properties of single-site probability distributions of the random potential and of the Integrated Density of States (IDS) in the Anderson models with infinite-range interactions and arbitrary…
It is shown that in a large class of disordered systems with non-degenerate disorder, in presence of non-local interactions, the Integrated Density of States (IDS) is at least H\"older continuous in one dimension and universally infinitely…
In this paper we discuss the continuity properties of the integrated density of states for random models based on that of the single site distribution. Our results are valid for models with independent randomness with arbitrary free parts.…
We prove that the integrated density of states (IDS) of random Schr\"{o}dinger operators with Anderson-type potentials on $L^2 (\R^d)$, for $d \geq1$, is locally H\"{o}lder continuous at all energies with the same H\"{o}lder exponent…
We survey some aspects of the theory of the integrated density of states (IDS) of random Schroedinger operators. The first part motivates the problem and introduces the relevant models as well as quantities of interest. The proof of the…
In this work we consider the Anderson model on $\ell^2(\mathbb{Z}^d)$ when the single site distribution (SSD) is given by $\mu_1 * \mu_2$, where $\mu_1$ is the Cauchy distribution and $\mu_2$ is any probability measure. For this model we…
We survey recent results on spectral properties of random Schr\"odinger operators. The focus is set on the integrated density of states (IDS). First we present a proof of the existence of a self-averaging IDS which is general enough to be…
We investigate how free probability allows us to approximate the density of states in tight binding models of disordered electronic systems. Extending our previous studies of the Anderson model in neighbor interactions [J. Chen et al.,…
We consider the $d$-dimensional Anderson model, and we prove the density of states is locally analytic if the single site potential distribution is locally analytic and the disorder is large. We employ the random walk expansion of…
For the weakly interacting one-dimensional multi-particle Anderson model in the continuum space of configurations, we prove the spectral exponential and the strong dynamical localization. The results require the interaction amplitude to be…
We consider the multi-particle Anderson model on the lattice with infinite range but sub-exponentially decaying interaction and show the Anderson localization consisting of the spectral exponential and the strong dynamical localization. In…
We first analyze the integrated density of states (IDS) of periodic Schr\"odinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with…
In this work we consider the Anderson model on Bethe lattice and prove that the integrated density of states (IDS) is as smooth as the single site distribution (SSD), in high disorder
We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of…
We show analytically that the apparent non-analyticity discovered recently in the inverse participation ratio (IPR) of the eigenstates in Anderson's model of localization is also present in a simple two-site model, along with a concurrent…
Taking into account that a proper description of disordered systems should focus on distribution functions, the authors develop a powerful numerical scheme for the determination of the probability distribution of the local density of states…
The asymptotic behavior of the integrated density of states (IDS), \(N(E)\), is investigated for random Schr\"{o}dinger operators with a single-site potential \(V\) satisfying \(\mathrm{essinf}\, V = -\infty\). Under the assumption that the…
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 the Integrated Density of States (IDS) of the random Schr\"odinger operator appearing in the study of certain reinforced random processes in connection with a supersymmetric sigma-model. We rely on previous results on the…
Numerical approaches to Anderson localization face the problem of having to treat large localization lengths while being restricted to finite system sizes. We show that by finite-size scaling of the probability distribution of the local…