Log-integrability of Rademacher Fourier series and applications to random analytic functions

Seminar: 
Combinatorics Seminar
Event time: 
Friday, March 7, 2014 - 9:00am to 10:00am
Location: 
215 LOM
Speaker: 
Alon Nishry
Speaker affiliation: 
Tel Aviv
Event description: 

We prove that the logarithm of Fourier series with random signs is integrable to any positive power.
Using this result we answer a long-standing question by J.-P. Kahane, concerning the range of random power series in the unit disk. In addition, we use this result to prove the angular equidistribution of the zeros of entire functions with random signs.

This is a joint work with F. Nazarov and M. Sodin.