60 citations · 91 across the 7 of their papers we have counts for
4 papers · 1 filter
Counting open nodal lines of random waves on planar domains
John A. Toth, Igor Wigman
We compute the asymptotic expectation of the number of {\em open} nodal lines for random waves on smooth planar domains. We find that for both the long energy window and th…
On the distribution of the nodal sets of random spherical harmonics
Igor Wigman
We study the length of the nodal set of eigenfunctions of the Laplacian on the $\spheredim$-dimensional sphere. It is well known that the eigenspaces corresponding to $\eigval=n(n+…
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…