On the recurrence set of planar Markov Random Walks

TL;DR

This paper explores the properties of recurrent points in planar Markov random walks using local limit theorems and spectral methods, providing new insights into their recurrence behavior.

Contribution

It introduces a spectral approach to analyze the recurrence set of planar Markov random walks under local limit theorem conditions.

Findings

Identification of conditions for recurrence in planar Markov random walks

Application of spectral methods to establish local limit theorems

Examples demonstrating the recurrence properties under various CLT scenarios

Abstract

In this paper, we investigate the properties of recurrent planar Markov random walks. More precisely, we study the set of recurrent points with the use of local limit theorems. The Nagaev-Guivarc'h spectral method provides several examples for which these local limit theorems are satisfied as soon as the (standard or non-standard) central limit theorem holds.