Related papers: Simplicity of eigenvalues in the Anderson model

We use a bootstrap argument to enhance the eigensystem multiscale analysis, introduced by Elgart and Klein for proving localization for the Anderson model at high disorder. The eigensystem multiscale analysis studies finite volume…

We prove a result of delocalization for the Anderson model on the regular tree (Bethe lattice). When the disorder is weak, it is known that large parts of the spectrum are a.s. purely absolutely continuous, and that the dynamical transport…

We prove that certain random models associated with radial, tree-like, rooted quantum graphs exhibit Anderson localization at all energies. The two main examples are the random length model (RLM) and the random Kirchhoff model (RKM). In the…

In this paper, we establish Anderson localization for the Maryland model with long range interactions.

In this note, we present a simpler way to prove the compactness of the closed intervals in simply ordered set with order topology.

The Typical Medium Theory provides conceptually the simplest order parameter description of Anderson localization by self-consistently calculating the geometrically-averaged (typical) local density of states (LDOS). Here we show how spatial…

The three-dimensional Anderson model represents a paradigmatic model to understand the Anderson localization transition. In this work we first review some key results obtained for this model in the past 50 years, and then study its…

We prove the almost sure existence of absolutely continuous spectrum at low disorder for the Anderson model on the simplest example of a product of a regular tree with a finite graph. This graph contains loops of unbounded size.

We introduce a number of random matrix models describing the Google matrix G of directed networks. The properties of their spectra and eigenstates are analyzed by numerical matrix diagonalization. We show that for certain models it is…

We prove a formula for special L-values of Anderson's modules, analogue in positive characteristic of the class number formula. We apply this result to two kinds of L-series.

We prove the occurrence of Anderson localisation for a system of infinitely many particles interacting with a short range potential, within the ground state Hartree-Fock approximation. We assume that the particles hop on a discrete lattice…

We introduce a family of trees that interpolate between the Bethe lattice and $\bbZ$. We prove complete localization for the Anderson model on any member of that family.

In the theory of Anderson localization, a landscape function predicts where wave functions localize in a disordered medium, without requiring the solution of an eigenvalue problem. It is known how to construct the localization landscape for…

A type analysable in one-based types in a simple theory is itself one-based.

We introduce an approach for exploring eigenvector localization phenomena for a class of (unbounded) selfadjoint operators. More specifically, given a target region and a tolerance, the algorithm identifies candidate eigenpairs for which…

We study the global existence of the singular nonlinear parabolic Anderson model equation on $2$-dimensional tours $\mathbb{T}^2$. The method is based on paracontrolled distribution and renormalization. After split the original nonlinear…

The self-consistent theory of localization is generalized to account for a weak quadratic nonlinear potential in the wave equation. For spreading wave packets, the theory predicts the destruction of Anderson localization by the nonlinearity…

We show that, with very high probability, the random graph Laplacian has simple spectrum. Our method provides a quantitatively effective estimate of the spectral gaps. Along the way, we establish results on affine no-gaps delocalization,…

This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…

We prove a.s. (almost sure) unisolvency of interpolation by continuous random sampling with respect to any given density, in spaces of multivariate a.e. (almost everywhere) analytic functions. Examples are given concerning polynomial and…