Related papers: Spectra of Anderson type models with decaying rand…
Spectral singularities are predicted to occur in a non-Hermitian extension of the Friedrichs-Fano-Anderson model describing the decay of a discrete state $|a >$ coupled to a continuum of modes. A physical realization of the model, based on…
In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and…
Scattering of light by a random stack of dielectric layers represents a one-dimensional scattering problem, where the scattered field is a three-dimensional vector field. We investigate the dependence of the scattering properties (band gaps…
We consider a simple model which is a caricature of a crystal interacting with a radiation field. The model has two bands of continuous spectrum and the particle can pass from the upper one to the lower by radiating a photon, the coupling…
Under mild non-degeneracy assumptions on branching rates in each generation, we provide a criterion for almost-sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total…
We consider the multi-particle Anderson model in the continuum and show that under some mild assumptions on the inter-particle interaction and the external potential, its lower spectral edge is almost surely constant and is the same with…
We prove an upper bound for the (differentiated) density of states of the Anderson model at the bottom of the spectrum. The density of states is shown to exhibit the same Lifshitz tails upper bound as the integrated density of states.
In this work, we study the spectral statistics for Anderson model on $\ell^2(\mathbb{N})$ with decaying randomness whose single site distribution has unbounded support. Here we consider the operator $H^\omega$ given by $(H^\omega…
This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…
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…
The aim of this paper is to show how free probability theory sheds light on spectral properties of deformed matricial models and provides a unified understanding of various asymptotic phenomena such as spectral measure description,…
We consider single-particle spectra of a symmetric narrow-band Anderson impurity model, where the host bandwidth $D$ is small compared to the hybridization strength $\Delta_{0}$. Simple 2nd order perturbation theory (2PT) in $U$ is found to…
We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more…
We show that charged-particles decaying in the early Universe can induce a scale-dependent or `running' spectral index in the small-scale linear and nonlinear matter power spectrum and discuss examples of this effect in minimal…
We investigate Anderson localization of light as occurring in ultra-short excitations. A theory based on time dependent coupled-mode equations predicts universal features in the spectrum of the transmitted pulse. In particular, the process…
We prove delocalization for the Anderson model on an infinite regular tree (or Cayley graph or Bethe lattice) at low disorder. This extends earlier results of Klein and Aizenman--Warzel by filling in the previously missing parts of the…
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…
This paper is devoted to the asymptotics of the density of surfacic states near the spectral edges for a discrete surfacic Anderson model. Two types of spectral edges have to be considered : fluctuating edges and stable edges. Each type has…
In this work we consider the Anderson model on the $d$-dimensional lattice with the single site potential having singular distribution, mainly $\alpha$-H\"older continuous ones and show that the eigenvalue statistics is Poisson in the…
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…