108 citations · 814 across the 70 of their papers we have counts for
10 papers · 1 filter
Nodal intersections for random eigenfunctions on the torus
Zeev Rudnick, Igor Wigman
We investigate the number of nodal intersections of random Gaussian Laplace eigenfunctions on the standard two-dimensional flat torus ("arithmetic random waves") with a fixed real-…
On the eigenvalue spacing distribution for a point scatterer on the flat torus
Zeev Rudnick, Henrik Ueberschaer
We study the level spacing distribution for the spectrum of a point scatterer on a flat torus. In the 2-dimensional case, we show that in the weak coupling regime the eigenvalue sp…
Almost all eigenfunctions of a rational polygon are uniformly distributed
Jens Marklof, Zeev Rudnick
We consider an orthonormal basis of eigenfunctions of the Dirichlet Laplacian for a rational polygon. The modulus squared of the eigenfunctions defines a sequence of probability me…
On the nodal sets of toral eigenfunctions
Jean Bourgain, Zeev Rudnick
We study the nodal sets of eigenfunctions of the Laplacian on the standard d-dimensional flat torus. The question we address is: Can a fixed hypersurface lie on the nodal sets of e…
On the volume of nodal sets for eigenfunctions of the Laplacian on the torus
Zeev Rudnick, Igor Wigman
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 $4π^2\eigenvalue$ with…
The Leray measure of nodal sets for random eigenfunctions on the torus
Ferenc Oravecz, Zeev Rudnick, Igor Wigman
We study nodal sets for typical eigenfunctions of the Laplacian on the standard torus in 2 or more dimensions. Making use of the multiplicities in the spectrum of the Laplacian, we…