05/24/2007 - 11:00

05/24/2007 - 12:00

Speaker:

Igor Wigman (CRM and McGill)

Location:

CRM, Room 5340

Abstract:

We study the volume of nodal sets for eigenfunctions of the Laplacian on the standard torus in two or more dimensions. We consider a sequence of eigenvalues with growing multiplicity , and compute the expectation and variance of the volume of the nodal set with respect to a Gaussian probability measure on the eigenspaces. We show that the expected volume of the nodal set is . Our main result is that the variance of the volume normalized by is bounded by , so that the normalized volume has vanishing fluctuations as we increase the dimension of the eigenspace.