A probabilistic language-free proof of an explicit Croot-Laba-Sisask Lemma

TL;DR

This paper presents a probabilistic, language-free proof of the Croot-Laba-Sisask Lemma, along with similar proofs for Khintchine and Marcinkiewicz-Zygmund inequalities, explicitly detailing the constants involved.

Contribution

It introduces a novel probabilistic, language-free approach to prove key inequalities and explicitly calculates the involved constants, enhancing understanding and applicability.

Findings

Probabilistic, language-free proof of Croot-Laba-Sisask Lemma

Explicit constants for Khintchine and Marcinkiewicz-Zygmund inequalities

Simplified proofs that avoid traditional language-based methods

Abstract

This note proposes a probabilistic language-free proof of the famous Croot-Laba-Sisask Lemma. In between, we do the same for the Khintchine and Marcinkiewicz-Zygmund inequalities and explicitate the implied constants.