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Zeroes of Gaussian stationary Functions

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Kolloquium SoSe 2022 Fachbereich Mathematik TU Darmstadt

Datum: 29.06.2022

Zeit: 17:15–18:15 Uhr

A* Gaussian stationary **function* is a centred collection of random variables {X_t} with multi-normal marginal distributions, for which the
covariance between X_t and X_s depends continuously only on |t-s|. Denote by Z(L) the number of zeroes of X_t in an interval of length L. The study
of this random variable was initiated by Kac and Rice in the 1940’s, who, pioneering random function theory, have recovered a formula for its
expectation. Since then, the theory has developed much further, with results on both typical and atypical behavior of Z(L) and numerous

During the last ten years, new perspectives on these classical questions have yielded general results with conceptual proofs and simple
formulation, providing much finer insight into Z(L).

In the talk we shall survey these developments, with a focus on the *typical behavior* of Z(L). In particular, we shall see a new simple form for its
variance, with some, potentially surprising, implications. No prior familiarity of Gaussian processes is assumed.


Naomi Feldheim, Bar-Ilan University, Israel


TU Darmstadt, S2|08 171 (Uhrturm-Hörsaal)
Hochschulstraße 4, 64298 Darmstadt


Technische Universität Darmstadt

Fachbereich Mathematik - Stochastik
Schlossgartenstraße 7
64289 Darmstadt
Telefon: +49 6151 16-23380
Telefax: +49 6151 16-23381


Goethe-Universität Frankfurt am Main, Johannes Gutenberg-Universität Mainz

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