# Anderson localisation in stationary ensembles of quasiperiodic operators

## TL;DR

This paper demonstrates that in a broad class of stationary quasi-periodic Schrödinger operators, Anderson localization occurs at strong coupling, supported by a new mathematical bound on Gaussian process interpolation errors.

## Contribution

It introduces a novel lower bound on interpolation errors for stationary Gaussian processes, enabling proof of Anderson localization in complex quasi-periodic systems.

## Key findings

- Almost every ensemble element exhibits Anderson localization.
- Pure point spectrum is established at strong coupling.
- New mathematical bounds support the localization proof.

## Abstract

An ensemble of quasi-periodic discrete Schr\"{o}dinger operators with an arbitrary number of basic frequencies is considered, in a lattice of arbitrary dimension, in which the hull function is a realisation of a stationary Gaussian process on the torus. We show that, for almost every element of the ensemble, the quasi-periodic operator boasts Anderson localization with simple pure point spectrum at strong coupling. One of the ingredients of the proof is a new lower bound on the interpolation error for stationary Gaussian processes on the torus (also known as local non-determinism).