Polynomial recurrence with large intersection over countable fields

TL;DR

This paper presents a concise proof demonstrating polynomial recurrence with large intersection for additive actions of vector spaces over countable fields, enhancing understanding of recurrence times in probability spaces.

Contribution

It provides a simplified proof that improves the known size and structure of strong recurrence times in polynomial recurrence over countable fields.

Findings

Enhanced bounds on recurrence times

Simplified proof technique

Improved understanding of recurrence structure

Abstract

We give a short proof of polynomial recurrence with large intersection for additive actions of finite-dimensional vector spaces over countable fields on probability spaces, improving upon the known size and structure of the set of strong recurrence times.