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Exponential Concentration for Zeroes of Stationary Gaussian Processes

Riddhipratim Basu^a, Amir Dembo^{b c}, Naomi Dvora Feldheim^{d e}✉, Ofer Zeitouni^{d e}

^aInternational Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore, India
^bDepartment of Mathematics, Stanford University, Stanford, CA, USA
^c[Department of Mathematics, Stanford University, Stanford, CA, USA]
^dDepartment of Mathematics, Weizmann Institute of Science, Rehovot, Israel
^eDepartment of Mathematics, Weizmann Institute of Science Rehovot, Israel
✉Corresponding author

International Mathematics Research Notices Oxford University Press2018-11-13 18 citations25 references

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Abstract

Abstract We show that for any centered stationary Gaussian process of absolutely 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.

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Exponential Concentration for Zeroes of Stationary Gaussian Processes

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