# Séminaires : Séminaire d'Analyse Fonctionnelle

 Equipe(s) : af, Responsables : E. Abakoumov - D. Cordero-Erausquin - G. Godefroy - O. Guédon - B. Maurey - G.Pisier Email des responsables : Salle : salle 13 - couloir 15-16 - 4ème étage Adresse : Campus Pierre et Marie Curie Description Le Jeudi à 10h30 -  IMJ-PRG - 4 place Jussieu - 75005 PARIS Lien vers les archives des années antérieures à 2015

 Orateur(s) Par Kurlberg - KTH Stockholm, Titre Nodal length statistics for arithmetic random waves Date 01/06/2017 Horaire 10:30 à 11:30 Diffusion Résume The Laplacian acting on the standard two dimensional torus has spectral multiplicities related to the number of ways an integer can be written as a sum of two integer squares. Using these multiplicities we can endow each eigenspace with a Gaussian probability measure. This induces a notion of a random eigenfunction (aka arithmetic random wave'') on the torus, and we study the statistics of the lengths of nodal sets (i.e., the zero set) of the eigenfunctions in the high energy limit''. In particular, we determine the variance for a generic sequence of energy levels, and also find that the variance can be different for certain degenerate'' subsequences; these degenerate subsequences are closely related to circles on which lattice points are very badly distributed. Time permitting we will discuss which probability measures on the unit circle that comes from'' lattice points on circles. Salle salle 13 - couloir 15-16 - 4ème étage Adresse Campus Pierre et Marie Curie