# Constanze Liaw: Rank-one perturbations and Anderson-type Hamiltonians

**Time: **
Wed 2019-05-29 13.15 - 14.15

**Location: **
F11, KTH

**Participating: **
Constanze Liaw (University of Delaware)

Abstract:

A rank-one perturbation A+K of an operator A is one where the range of K is just one-dimensional. Being rather restrictive, they form a small class of perturbations. Yet, rank-one perturbations are related to many deep questions in analysis and applications. Here we focus on a relation with Anderson-type Hamiltonians. These are operators involving random perturbations obtained by taking a countable sum of rank-one perturbations, each weighted by a randomly chosen coupling constant. Such perturbations are non-compact almost surely. Under mild conditions, the essential parts of two realizations of an Anderson-type Hamiltonian are almost surely related by a rank-one perturbation.