An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process

Eran Assaf; Jeremiah Buckley; Naomi Feldheim

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arXiv · 2101.04052

An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process

Eran Assaf·Jeremiah Buckley·Naomi Feldheim

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Abstract

We study the variance of the number of zeroes of a stationary Gaussian process on a long interval. We give a simple asymptotic description under mild mixing conditions. This allows us to characterise minimal and maximal growth. We show that a small (symmetrised) atom in the spectral measure at a special frequency does not affect the asymptotic growth of the variance, while an atom at any other frequency results in maximal growth. Our results allow us to analyse a large number of interesting examples.

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Eran Assaf, Jeremiah Buckley, Naomi Feldheim. 2021-01-11. An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process. https://arxiv.org/abs/2101.04052

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