Igor Wigman

On the Volume of Nodal Sets for Eigenfunctions of the Laplacian on the Torus

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 4π2E with growing multiplicity

On the distribution of the nodal sets of random spherical harmonics

{\mathcal{N}} \rightarrow \infty

On the area of excursion sets of spherical Gaussian eigenfunctions

, 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

The defect variance of random spherical harmonics

const{\sqrt{E}}

Fluctuations of the total number of critical points of random spherical harmonics

. Our main result is that the variance of the volume normalized by