# On complete localization for the one-dimensional multi-particle Anderson-Bernoulli model with infinite range interaction

## TL;DR

This paper proves Anderson localization for a multi-particle one-dimensional Anderson-Bernoulli model with infinite-range, sub-exponentially decaying interactions, including spectral and strong dynamical localization in Hilbert-Schmidt norm.

## Contribution

It establishes localization results for a multi-particle Anderson model with very singular Bernoulli-type distributions and infinite-range interactions, extending previous localization theories.

## Key findings

- Spectral exponential localization proven
- Strong dynamical localization established in Hilbert-Schmidt norm
- Applicable to models with Bernoulli measures and infinite-range interactions

## Abstract

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 particular, the dynamical localization is proved int he Hilbert-Schmidt norm. The results concern very singular probability distributions such as the Bernoulli's measures.