## Abstract

We prove an optimal one-volume Wegner estimate for interacting systems of N quantum particles moving in the presence of random potentials. The proof is based on the scale-free unique continuation principle recently developed for the 1-body problem by Roj as-Molina and Veselic [17] and extended to spectral projectors by Klein [12]. These results extend our previous results in [8,9]. We also prove a two-volume Wegner estimate as introduced in [5]. The random potentials are generalized Anderson-type potentials in each variable with minimal conditions on the single-site potential aside from positivity. Under additional conditions, we prove the Lipschitz continuity of the integrated density of states (IDS). This implies the existence and local finiteness of the density of states. We also apply these techniques to interacting iV-particle Schrodinger operators with Delone-Anderson type random external potentials.

Original language | English |
---|---|

Pages (from-to) | 519-536 |

Number of pages | 18 |

Journal | Markov Processes and Related Fields |

Volume | 21 |

Issue number | 3 |

State | Published - 2015 |

### Bibliographical note

Publisher Copyright:© Polymat, Moscow 2015.

## Keywords

- Localization
- Many-body quantum theory
- Random operators

## ASJC Scopus subject areas

- Statistics and Probability
- Applied Mathematics