## Persistence Exponents for Gaussian stationary functions

Series
Analysis Seminar
Time
Wednesday, February 2, 2022 - 2:00pm for 1 hour (actually 50 minutes)
Location
Speaker
Naomi Feldheim – Bar-Ilan University – naomi.feldheim@biu.ac.il
Organizer

Let f be a real-valued Gaussian stationary process, that is, a random function which is invariant to real shifts and whose marginals have multi-normal distribution.

What is the probability that f remains above a certain fixed line for a long period of time?

We give simple spectral(and almost tight) conditions under which this probability is asymptotically exponential, that is, that the limit of log P(f>a on [0,T])/ T, as T approaches infinity, exists.

This limit defines "the persistence exponent", and we further show it is continuous in the level a, in the spectral measure corresponding to f (in an appropriate sense), and is unaffected by the singular part of the spectral measure.

Proofs rely on tools from harmonic analysis.

Joint work with Ohad Feldheim and Sumit Mukherjee, arXiv:2112.04820.

The talk will be on Zoom via the link

https://us02web.zoom.us/j/71579248210?pwd=d2VPck1CbjltZStURWRWUUgwTFVLZz09