Colloquium: Tuesday, December 7, 2021. Speaker: Naomi Feldheim (Bar-Ilan). Title: “A spectral perspective on Gaussian stationary processes”.

The next colloquium for this semester will be held ONLINE on 7.12.2021 at 14:00 (Tuesday).

Zoom link:

Speaker: Naomi Feldheim (Bar-Ilan University)

Date: Tuesday, December 7, 2021

Time: 14:00

Title: A spectral perspective on Gaussian stationary processes

Abstract: Consider a real Gaussian stationary process, either on Z or on R

(that is, a stochastic process, invariant under translations, whose finite marginals are centered multi-variate Gaussians).

What is the probability that it remains positive on [0,N] for large N?

This question, and other similar ones, were largely open for at least 50 years, and in spite of numerous motivations,

only rough bounds and few particular examples were known.

In several recent works substantial progress has been made, mainly due to a “spectral perspective”

and the employment of tools from real and harmonic analysis.

In the talk I will describe this spectral point of view and how it is used to analyse

the qualitative behavior of such rare events.

Based on joint works with several co-authors.

No knowledge of Gaussian processes will be assumed.