Thin sets of integers in Harmonic analysis and p-stable random Fourier series

TL;DR

This paper explores how thin sets of integers behave in harmonic analysis and p-stable random Fourier series, revealing similarities to Gaussian cases in some scenarios and differences in others.

Contribution

It compares the behavior of thin sets under p-stable variables to Gaussian and Rademacher cases, highlighting cases of equivalence and divergence.

Findings

Behavior similar to Gaussian case for certain thin sets

Behavior differs significantly from Gaussian case in other scenarios

Provides insights into the impact of p-stability on harmonic analysis

Abstract

We investigate the behavior of some thin sets of integers defined through random trigonometric polynomial when one replaces Gaussian or Rademacher variables by p-stable ones, with 1 < p < 2. We show that in one case this behavior is essentially the same as in the Gaussian case, whereas in another case, this behavior is entirely different.