Overcrowding estimates for zero count and nodal length of stationary Gaussian processes

2020/12/20 by Priya, Lakshmi · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2012.10857

Abstract

Assuming certain conditions on the spectral measures of centered stationary Gaussian processes on ℝ (or ℝ²), we show that the probability of the event that their zero count in an interval (resp., nodal length in a square domain) is larger than n, where n is much larger than the expected value of the zero count in that interval (resp., nodal length in that square domain), is exponentially small in n.

Cited by

• Tightness of Stationary Nodal Measures

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