Event № 2173
Event № 2173
Type: Lecture
Name: ANALYSIS SEMINAR
Title: Spectral gap and sign changes of Gaussian stationary processes
Speaker: Dr. Naomi Feldheim
Place:
2nd floor Colloquium Room, Building 216 , Bar Ilan University
Abstract:
It is known that the Fourier transform of a measure which vanishes onIt is known that the Fourier transform of a measure which vanishes on [-a,a] must have asymptotically at least a/pi zeroes per unit interval. One way to quantify this further is using a probabilistic model: Let f be a Gaussian stationary process on R whose spectral measure vanishes on [-a,a]. What is the probability that it has no zeroes on an interval of length L? Our main result shows that this probability is at most e^{-c a^2 L^2}, where c>0 is an absolute constant. This settles a question which was open for a while in the theory of Gaussian processes.I will explain how to translate the probabilistic problem to a problem of minimizing weighted L^2 norms of polynomials against the spectral measure, and how we solve it using tools from harmonic and complex analysis. Time permitting, I will discuss lower bounds. Based on a joint work with Ohad Feldheim, Benjamin Jaye, Fedor Nazarov and Shahaf Nitzan (arXiv:1801.10392).
SubmittedBy:
Elijah Liflyand , liflyand@gmail.com
EventLink: Event № 2173