| 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 |
