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Mathematische Gesellschaft
Quantum ergodicity
13.7.2017, 16:15 - 17:15
Speaker:Prof. Dr. Nalini Anantharaman, Université de Strasbourg
Location:Mathematisches Institut, Bunsenstr 3-5SitzungszimmerGras Geo Map
Organizer:Mathematisches Institut
Abstract: ``Quantum ergodicity'' usually deals with the study of eigenfunctions of the Laplacian on Riemannian manifolds, in the high-frequency asymptotics.
Under certain geometric assumptions (such as negative curvature), the idea is that the eigenfunctions should become spatially uniformly distributed, in the high-frequency limit. I will review the many conjectures in the subject, some of which have been turned into theorems recently. Physicists like Uzy Smilansky or John Keating have suggested looking for similar questions and results on large (finite) discrete graphs. Take a large graph $G=(V, E)$ and an eigenfunction $\psi$ of the discrete Laplacian -- normalized in $L^2(V)$. What can we say about the probability measure $|\psi(x)|^2$ ($x\in V$)? Is it close to uniform, or on the contrary can it be concentrated in small sets? I will talk about with Etienne Le Masson, for large regular graphs, and with Mostafa Sabri in the non-regular case
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