43 citations · 130 across the 29 of their papers we have counts for
4 papers · 1 filter
Poisson approximation of the largest gaps between zeros of a stationary Gaussian process
Renjie Feng, Stephen Muirhead
We study the largest gaps between successive zeros of a smooth stationary Gaussian process. Our main result is that, if correlations decay at least polynomially, then after suitabl…
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…
The maximum of a strongly correlated Gaussian process
Jason Li, Stephen Muirhead
We revisit a result of Mittal--Ylvisaker that states that the rescaled maximum of a stationary sequence of Gaussian random variables has a Gaussian limit if correlations decay suff…
Persistence and entropic repulsion of stationary Gaussian fields with spectral singularity at the origin
Naomi Feldheim, Ohad Feldheim, Stephen Muirhead
We compute the exact log-asymptotics of the persistence probability, and determine the entropic repulsion profile conditioned on persistence, for general -dimensional stationary…