# Wegner bounds for one-dimensional multi-particle Bernoulli-Anderson models in the continuum

## TL;DR

This paper establishes Wegner bounds for one-dimensional multi-particle Anderson models with singular distributions like Bernoulli, demonstrating localization under weak interactions through multi-scale analysis.

## Contribution

It provides the first Wegner bounds for multi-particle continuum models with Bernoulli distributions, extending localization results to singular measures.

## Key findings

- Wegner bounds proven for Bernoulli distributions in multi-particle models
- Localization established via multi-scale analysis under weak interactions
- Applicable to singular probability measures in continuum models

## Abstract

We prove the Wegner bounds for the one-dimensional interacting multi-particle Anderson models in the continuum. The results apply to singular probability distribution functions such as the Bernoulli's measures. The proofs need the amplitude of the inter-particle interaction potential to be sufficiently weak. As a consequence, the results imply the Anderson localization via the multi-scale analysis.