Naomi Feldheim (Bar Ilan University)

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

vendredi 11 juin 2021, 9h30 - 10h30


Suppose that we are given the covariance function of a stationary Gaussian process on the real line. The mean number of zeroes in an interval is given by the famous Kac-Rice formula. Can we compute the variance? – Unfortunately, not as easily. Expressions for the variance were given by Cramer-Leadbetter and Kratz-Leon, but the asymptotic growth as the interval grows longer is not apparent from them. In this talk we will give an asymptotic formula for the variance, which holds under mild mixing conditions. We will also discuss atoms in the spectral measure, the emergence of a `special frequency’, and some interesting examples. Joint work with Eran Assaf and Jeremiah Buckley (