69 citations · 495 across the 46 of their papers we have counts for
59 papers
Sign-balance of random Laplace eigenfunctions
Stephen Muirhead, Igor Wigman
Motivated by the problem of the small-scale sign distribution of Laplace eigenfunctions, we introduce a strong notion of sign-balance for (eigen)functions, and prove that random ei…
On the supremum of random cusp forms
Bingrong Huang, Stephen Lester, Igor Wigman +1
A random ensemble of cusp forms for the full modular group is introduced. For a weight- cusp form, restricted to a compact subdomain of the modular surface, the true order of ma…
The giant component of excursion sets of spherical Gaussian ensembles: existence, uniqueness, and volume concentration
Stephen Muirhead, Igor Wigman
We establish the existence and uniqueness of a well-concentrated giant component in the supercritical excursion sets of three important ensembles of spherical Gaussian random field…
Eigenvalue clusters for the hemisphere Laplacian with variable Robin condition
Alexander Pushnitski, Igor Wigman
We study the eigenvalue clusters of the Robin Laplacian on the 2-dimensional hemisphere with a variable Robin coefficient on the equator. The 'th cluster has eigenva…
Around the Gauss circle problem: Hardy's conjecture and the distribution of lattice points near circles
Stephen Lester, Igor Wigman
Hardy conjectured that the error term arising from approximating the number of lattice points lying in a radius- disc by its area is . One source of support for…
Almost sure GOE fluctuations of energy levels for hyperbolic surfaces of high genus
Zeév Rudnick, Igor Wigman
We study the variance of a linear statistic of the Laplace eigenvalues on a hyperbolic surface, when the surface varies over the moduli space of all surfaces of fixed genus, sample…