An easy proof of Polya's theorem on random walks

TL;DR

This paper provides a simplified proof of Polya's theorem, demonstrating that a two-dimensional lattice random walk almost surely returns to its origin.

Contribution

It offers an accessible proof of Polya's theorem, making the concept more understandable and easier to verify.

Findings

Random walks on 2D lattices are recurrent with probability one.

The proof simplifies understanding of Polya's theorem.

Supports the theoretical foundation of random walk recurrence.

Abstract

We present an easy proof of Polya's theorem on random walks: with the probability one a random walk on the two-dimensional lattice returns to the starting point.