Séminaires : Séminaire d'Analyse Fonctionnelle

Equipe(s) : af,
Responsables :E. Abakoumov - A.Eskenazis - D. Cordero-Erausquin - M. Fathi - O. Guédon - B. Maurey
Email des responsables :
Salle : salle 13 - couloir 15-16 - 4ème étage
Adresse :Campus Pierre et Marie Curie
Le Jeudi à 10h30 -  IMJ-PRG - 4 place Jussieu - 75005 PARIS

Orateur(s) Par Kurlberg - KTH Stockholm,
Titre Nodal length statistics for arithmetic random waves
Horaire10:30 à 11:30
RésumeThe 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.
Sallesalle 13 - couloir 15-16 - 4ème étage
AdresseCampus Pierre et Marie Curie