5 papers
Excursion Fluctuations and Spectral Universality in Gaussian Fields
Dmitry Beliaev, Akshay Hegde
We study the large-scale spatial fluctuations of excursion volumes for a class of smooth stationary Gaussian fields. In the case of Berry's random wave model in dimension $d \geq 2…
High local maxima of stationary smooth Gaussian fields
Dmitry Beliaev, Akshay Hegde
Consider the point process (in ) of local maxima of smooth Gaussian fields, with sufficient decay of correlation at infinity, above a level . We show that this poi…
A covariance formula for topological events of smooth Gaussian fields
Dmitry Beliaev, Stephen Muirhead, Alejandro Rivera
We derive a covariance formula for the class of `topological events' of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets of…
A covariance formula for the number of excursion set components of Gaussian fields and applications
Dmitry Beliaev, Michael McAuley, Stephen Muirhead
We derive a covariance formula for the number of excursion or level set components of a smooth stationary Gaussian field on contained in compact domains. We also pre…
A central limit theorem for the number of excursion set components of Gaussian fields
Dmitry Beliaev, Michael McAuley, Stephen Muirhead
For a smooth stationary Gaussian field on and level , we consider the number of connected components of the excursion set (or l…