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math.PR2026
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…
math.PR2026
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…