Non-backtracking random walk

TL;DR

This paper analyzes non-backtracking random walks on lattices and tori, deriving spectral properties and proving a central limit theorem, which enhances understanding of their long-term behavior and convergence rates.

Contribution

It provides a spectral analysis of NBW transition matrices and establishes a functional central limit theorem for NBW on Zd.

Findings

Spectral properties of NBW transition matrices derived.

Functional central limit theorem proved for NBW on Zd.

Convergence estimates towards stationary distribution on tori obtained.

Abstract

We consider non-backtracking random walk (NBW) in the nearest-neighbor setting on the Zd-lattice and on tori. We evaluate the eigensystem of the m X m-dimensional transition matrix of NBW where m denote the degree of the graph. We use its eigensystem to show a functional central limit theorem for NBW on Zd and to obtain estimates on the convergence towards the stationary distribution for NBW on the torus.