Random differences in Szemer\'edi's theorem and related results

TL;DR

This paper presents a new elementary method for analyzing random differences in arithmetic progressions and convergence along random sequences, leading to improved results in this area.

Contribution

The authors introduce a novel elementary approach to study random differences and convergence phenomena, advancing the understanding of arithmetic progressions in random settings.

Findings

Significant improvements on existing results

Effective method for studying random differences

Enhanced understanding of convergence along random sequences

Abstract

We introduce a new, elementary method for studying random differences in arithmetic progressions and convergence phenomena along random sequences of integers. We apply our method to obtain significant improvements on previously known results.