Related papers: Lifshitz tails on the Bethe lattice: a combinatori…
We derive bounds on the integrated density of states for a class of Schr\"odinger operators with a random potential. The potential depends on a sequence of random variables, not necessarily in a linear way. An example of such a random…
We consider the Dirichlet Laplacian $H_\gamma$ on a 3D twisted waveguide with random Anderson-type twisting $\gamma$. We introduce the integrated density of states $N_\gamma$ for the operator $H_\gamma$, and investigate the Lifshits tails…
We study the asymptotic behaviour of stationary densities of one-dimensional random diffeomorphisms, at the boundaries of their support, which correspond to deterministic fixed points of extremal diffeomorphisms. In particular, we show how…
We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density…
The density of states of Dirac fermions with a random mass on a two-dimensional lattice is considered. We give the explicit asymptotic form of the single-electron density of states as a function of both energy and (average) Dirac mass, in…
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…
We study Lifshitz tails for random Schr\"odinger operators where the random potential is alloy type in the sense that the single site potentials are independent, identically distributed, but they may have various function forms. We suppose…
We consider one-parameter families of random circle diffeomorphisms $g_{E,y}$ for which the unperturbed map $g_{0,\bar{0}}$ has a fixed point of order $2k$ and the dependence on the parameter $E$ is monotone. Under reasonable assumptions,…
We consider the problem of randomly distributed positive delta-function scatterers in a strong magnetic field and study the behavior of density of states close to the spectral boundary at $E=\hbar\omega_{c}/2$ in both two and three…
The density of states, even for a perfectly ordered tight-binding model, can exhibit a tail-like feature at the top of the band, provided the hopping integral falls off in space slowly enough. We apply the coherent potential approximation…
We prove that the homogeneous hierarchical Anderson model exhibits a Lifshits tail at the upper edge of its spectrum. The Lifshits exponent is given in terms of the spectral dimension of the homogeneous hierarchical structure. Our approach…
Non-Hermitean operators may appear during the calculation of a partition function in various models of statistical mechanics. The tail eigen-states, having anomalously small real part of energy $Re(\eps)$, became naturally important in this…
In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and $p$-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar…
We investigate Lifshits-tail behaviour of the integrated density of states for a wide class of Schr\"odinger operators with positive random potentials. The setting includes alloy-type and Poissonian random potentials. The considered…
We consider the annealed asymptotics for the survival probability of Brownian motion among randomly distributed traps. The configuration of the traps is given by independent displacements of the lattice points. We determine the long time…
Limits of densities belonging to an exponential family appear in many applications, {e.g.} Gibbs models in Statistical Physics, relaxed combinatorial optimization, coding theory, critical likelihood computations, Bayes priors with singular…
The current paper is devoted to the study of existence, uniqueness and Lifshitz tails of the integrated density of surface states (IDSS) for Schr\"{o}dinger operators with alloy type random surface potentials. We prove the existence and…
Robust edge transport can occur when particles in crystalline lattices interact with an external magnetic field. This system is well described by Bloch's theorem, with the spectrum being composed of bands of bulk states and in-gap edge…
We study the one-dimensional tight-binding models which include a slowly varying, incommensurate off-diagonal modulation on the hopping amplitude. Interestingly, we find that the mobility edges can appear only when this off-diagonal…
We show that continuous random walks (diffusion) in the Poincar\'{e} hyperbolic upper halfplane $\mathbb{H}^2 = \{(x,y)|y>0\}$ provide a unifying description of three seemingly unrelated phenomena: (i) the non-analytic divergence of the…