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

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.

10 pages. arXiv admin note: text overlap with arXiv:1612.08303

References in corpus (3)

• Wegner bounds for a two-particle tight binding model
• On two-particle Anderson localization at low energies
• Optimal Wegner estimate and the density of states for N-body, interacting Schrodinger operators with random potentials