Exponential concentration for zeroes of stationary Gaussian processes

Riddhipratim Basu, Amir Dembo, Naomi Feldheim, Ofer Zeitouni

Published 2017-09-20Version 1

We show that for any centered stationary Gaussian process of integrable covariance, whose spectral measure has compact support, or finite exponential moments (and some additional regularity), the number of zeroes of the process in $[0,T]$ is within $\eta T$ of its mean value, up to an exponentially small in $T$ probability.