相关论文: Continuity of integrated density of states -- inde…

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…

Following [5], 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. In the present work, we…

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…

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 study a class of continuous matrix-valued Anderson models acting on $L^{2}(\R^{d})\otimes \C^{N}$. We prove the existence of their Integrated Density of States for any $d\geq 1$ and $N\geq 1$. Then for $d=1$ and for arbitrary $N$, we…

We establish several properties of the integrated density of states for random quantum graphs: Under appropriate ergodicity and amenability assumptions, the integrated density of states can be defined using an exhaustion procedure by…

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…

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 derive quantitative continuity estimates for the higher-order derivatives of the integrated density of states (IDS) with respect to the disorder parameter for the Anderson model on $\ell^2(\mathbb{G})$. Here $\mathbb{G}=\mathbb{Z}^d$ or…

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 consider the Anderson model on the multi-dimensional cubic lattice and prove a positive lower bound on the density of states under certain conditions. For example, if the random variables are independently and identically distributed and…

In this paper, we study the non-self-dual extended Harper's model with a Liouville frequency. Based on the work of \cite{SY}, we show that the integrated density of states (IDS for short) of the model is $\frac{1}{2}$-H$\ddot{\text{o}}$lder…

We study the root-averaged density of states for the Anderson model on the Bethe lattice in the strong-disorder regime. Here the density of states means the root-averaged spectral measure, not a finite-volume eigenvalue counting limit. We…

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…

We prove that the integrated density of surface states of continuous or discrete Anderson-type random Schroedinger operators is a measurable locally integrable function rather than a signed measure or a distribution. This generalize our…

We introduce and prove local Wegner estimates for continuous generalized Anderson Hamiltonians, where the single-site random variables are independent but not necessarily identically distributed. In particular, we get Wegner estimates with…

In this paper we consider some Anderson type models, with decaying randomness and the free parts having long range tails. The randomness may decay at different rates in different directions, though in majority of directions we require some…

We consider diagonal disordered one-dimensional Anderson models with an underlying periodicity. We assume the simplest periodicity, i.e., we have essentially two lattices, one that is composed of the random potentials and the other of…

Results of large-scale numerical simulations are reported on the Anderson localization in a two-dimensional square lattice tight-binding model with random flux. Localization lengths, fluctuations of the conductance, and the density of…

We prove that the the density of states measure (DOSm) for random Schr\"odinger operators on $\mathbb{Z}^d$ is weak-$^*$ H\"older-continuous in the probability measure. The framework we develop is general enough to extend to a wide range of…