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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…