New results on Rademacher Fourier and Taylor series

Update: 2012-09-24

Description

This is a report on a joint work in progress with Fedor Nazarov and Alon Nishry. We prove that any power of the logarithm of Rademacher Fourier series (i.e. a square summable Fourier series with random independent signs) is integrable. This result has several applications to zeroes and value-distribution of random Talor series. One of this applications gives asymptotics for the counting function of zeroes of arbitrary Taylor series with random independent signs, and proves their angular equidistribution. Another application answers an old question by J.-P.Kahane.

Comments

Top Podcasts

The Best New Comedy Podcast Right Now – June 2024 The Best News Podcast Right Now – June 2024 The Best New Business Podcast Right Now – June 2024 The Best New Sports Podcast Right Now – June 2024 The Best New True Crime Podcast Right Now – June 2024 The Best New Joe Rogan Experience Podcast Right Now – June 20 The Best New Dan Bongino Show Podcast Right Now – June 20 The Best New Mark Levin Podcast – June 2024

In Channel

Progress in rigorous multi-particle localization: Simpler proofs of stronger results

2012-09-2541:59

Spreading in potentials random in space and time

2012-09-2540:07

The low lying spectrum of one-dimensional random models

2012-09-2544:13

Near integrable systems

2012-09-2540:53

Enhancement of Superconductivity by Anderson Localization

2012-09-2544:10

Statistical mechanics approach to the random matrix models

2012-09-2543:21

Anderson localization, topology, and interaction

2012-09-2441:41

Universality of the second mixed moment of the characteristic polynomials of the 1D Gaussian band matrices

2012-09-2442:03

Universal statistics for directed polymers and the KPZ equation from the replica Bethe Ansatz

2012-09-2443:02

New results on Rademacher Fourier and Taylor series

2012-09-2433:30

Diffusion for a quantum particle coupled to a phonon gas

2012-09-2443:49

Supersymmetry in localization/delocalization problems

2012-09-2442:54

Localization for Linearly Reinforced Random Walks and Vertex Reinforced Jump Processes (iii)

2012-09-2439:06

Kolmogorov turbulence, Anderson localization and KAM integrability

2012-09-2445:04

Anomalously localized states in the one-dimensional Anderson localization model at E=0

2012-09-2443:53

Edge reinforced random walks, Vertex reinforced jump process and the SuSy hyperbolic sigma model (II)

2012-09-2141:25

Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function

2012-09-2139:08

Classification and symmetry properties of scaling dimensions at Anderson transitions

2012-09-2144:40

Recent progress in the spectral theory of first order elliptic systems

2012-09-2140:59

Topological phases of matter, Anderson localization/delocalization and anomalous transport law

2012-09-2141:30

00:00

New results on Rademacher Fourier and Taylor series

#box-pro-ellipsis-173247567926685{-webkit-line-clamp:2;}New results on Rademacher Fourier and Taylor series

New results on Rademacher Fourier and Taylor series

Cambridge University

New results on Rademacher Fourier and Taylor series