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# Quantum ergodicity on large graphs

## Advances in Homogeneous Dynamics May 11, 2015 - May 15, 2015

May 11, 2015 (11:10 AM PDT - 12:00 PM PDT)
Speaker(s): Nalini Anantharaman (Université de Strasbourg)
Location: MSRI: Simons Auditorium
Tags/Keywords
• probabilistic methods in ergodicity

• geodesic flow

• compact Riemannian manifold

• quantum variance of operators

• negative curvature manifolds

• graph-theoretic generalization

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

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Abstract

We study eigenfunctions of the discrete laplacian on large regular graphs, and prove a quantum ergodicity'' result for these eigenfunctions : for most eigenfunctions $\psi$, the probability measure $|\psi(x)|^2$, defined on the set of vertices, is close to the uniform measure.

Although our proof is specific to regular graphs, we'll discuss possibilities of adaptation to more general models, like the Anderson model on regular graphs.

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