Delocalization in the Anderson's model on trees

par Dylan Thevenet

lundi 5 janv. 2026, 10:30 → 11:25 Europe/Paris

Fokko du Cloux (ICJ)

In order to describe the behavior of a quantum particle in a disordered environment, Anderson proposed a model in 1958 in which disorder is represented by a random potential. More formally, we will assume that the particle moves on the vertices of a graph and its motion is governed by the operator H = -Δ + V, where V is a collection of i.i.d. random variables indexed by the vertices of the graph. To understand the behavior of the particle, we need to understand the spectral properties of the operator H.

In this talk, I will begin by discussing spectral theory for bounded operators on a Hilbert space in order to define the notions of purely pointwise, absolutely continuous, and singularly continuous spectrum. I will then develop some tools to demonstrate that there remains an absolutely continuous spectrum phase on trees.