Exponential concentration for zeroes of stationary Gaussian processes

2017/09/20 by Basu, Riddhipratim, Dembo, Amir, Feldheim, Naomi +1
#42A38 (Secondary) #60F10 (Primary) 60G10 #60G15 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1709.06760

Abstract

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 ηT of its mean value, up to an exponentially small in T probability.

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