## Abstract

We prove that certain natural random variables associated with the local eigenvalue statistics for generalized lattice Anderson models constructed with finite-rank perturbations are compound Poisson distributed. This distribution is characterized by the fact that the Lévy measure is supported on at most a finite set of positive integers determined by the rank. The proof relies on a Minami-type estimate for finite-rank perturbations. For Anderson-type continuum models on $${{\mathbb{R}^d}}$$^{Rd}, we prove a similar result for certain natural random variables associated with the local eigenvalue statistics. We prove that the compound Poisson distribution associated with these random variables has a Lévy measure whose support is at most the set of positive integers.

Original language | English |
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Pages (from-to) | 125-143 |

Number of pages | 19 |

Journal | Communications in Mathematical Physics |

Volume | 340 |

Issue number | 1 |

DOIs | |

State | Published - Nov 14 2015 |

### Bibliographical note

Publisher Copyright:© 2015, Springer-Verlag Berlin Heidelberg.

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics