3 papers
math.PR2026
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…
math.PR2025
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…
math.NT2025
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…