Séminaire Analyse Harmonique
GOE and GUE statistics on random hyperbolic surfaces
April 2023
Intervenant : Frédéric Naud
Institution : Sorbonne Université
Heure : 14h00 - 15h00
Lieu : salle 2L8

We will describe some models of Random compact hyperbolic surfaces on which it is possible to study, in a large genus regime, the smooth linear spectral statistics for the (twisted) Laplace spectrum. We will show that the variance converges, after taking ad hoc limits, to the one given by the random matrix models of GOE and GUE. This is, in a fairly weak sense, a rigorous justification of some popular conjectures of quantum chaos from the 80's.

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