Hyperbolic self avoiding walk

TL;DR

This paper proves that self-avoiding walks in hyperbolic spaces tend to move ballistically, meaning they escape to infinity at a linear rate, highlighting unique geometric effects on such stochastic processes.

Contribution

It establishes the expected ballistic behavior of self-avoiding walks specifically in hyperbolic spaces, a novel setting for this type of stochastic process.

Findings

Self-avoiding walks in hyperbolic spaces are ballistic.

Expected escape rate of the walk is linear.

Hyperbolic geometry influences walk behavior significantly.

Abstract

Expected ballisticity of a continuous self avoiding walk on hyperbolic spaces $\mathbb{H}^d$ is established.