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

Non-equilibrium Dynamics and Random Matrices
Topic:Log-integrability of Rademacher Fourier series and applications to random analytic functions
Speaker:Alon Nishry
Affiliation:Member, School of Mathematics
Date:Tuesday, February 11
Time/Room:2:00pm - 3:00pm/S-101
Video Link:https://video.ias.edu/nedrm/2014/0211-AlonNishry

We prove that the logarithm of Fourier series with random signs is integrable to any positive power. We use this result to prove the angular equidistribution of the zeros of entire functions with random signs (and more generally the almost sure convergence of certain linear statistics of the zeros).