Related papers: The Anderson model with missing sites
This paper is devoted to the study of the random displacement model on $\R^d$. We prove that, in the weak displacement regime, Anderson and dynamical localization holds near the bottom of the spectrum under a generic assumption on the…
We prove localization (near the bottom of the spectrum) for certain non-stationary variants of the Anderson model in three dimensions. More specifically, we prove a Wegner estimate, which implies localization by existing work. Two key…
We study the multi-particle Anderson model in the continuum and show that under some mild assumptions on the random external potential and the inter-particle interaction, for any finite number of particles, the multi-particle lower edges of…
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…
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…
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 a one-dimensional Anderson model where the potential decays in average like $n^{-\alpha}$, $\alpha>0$. This simple model is known to display a rich phase diagram with different kinds of spectrum arising as the decay rate…
Delone operators are Schr\"odinger operators in multi-dimensional Euclidean space with a potential given by the sum of all translates of a given "single-site potential" centred at the points of a Delone set. In this paper, we use…
For the multi-particle Anderson model with correlated random potential in the continuum, we show under fairly general assumptions on the inter-particle interaction and the random external potential, the Anderson localization which consists…
We study spectral properties of partial differential operators modelling composite materials with highly contrasting constituents, comprised of soft spherical inclusions with random radii dispersed in a stiff matrix. Such operators have…
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…
We prove localization and probabilistic bounds on the minimum level spacing for the Anderson tight-binding model on the lattice in any dimension, with single-site potential having a discrete distribution taking N values, with N large.
We pinpoint the spectral decomposition for the Anderson tight-binding model with an unbounded random potential on the Bethe lattice of sufficiently large degree. We prove that there exist a finite number of mobility edges separating…
This review presents a unified view on the problem of Anderson localization in one-dimensional weakly disordered systems with short-range and long-range statistical correlations in random potentials. The following models are analyzed: the…
In this paper we consider an Anderson model with a large number of sites with zero interaction. For such models we study the spectral statistics in the region of complete localization. We show that Poisson statistics holds for such…
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…
Our recently established criterion for the formation of extended states on tree graphs in the presence of disorder is shown to have the surprising implication that for bounded random potentials, as in the Anderson model, there is no…
We report on recent results on the spectral statistics of the discrete Anderson model in the localized phase. Our results show, in particular, that, for the discrete Anderson Hamiltonian with smoothly distributed random potential at…
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 determine the phase diagram of the Anderson tight-binding model on random regular graphs with Gaussian disorder and sufficiently large degree. In particular, we prove that if the degree is fixed and the number of vertices goes to…