An Upper Bound on the critical density for Activated Random Walks on Euclidean Lattices

TL;DR

This paper establishes an upper bound of one on the critical density for activated random walks on Euclidean lattices, providing insight into the phase transition behavior of this stochastic process.

Contribution

The paper proves a new upper bound on the critical density for activated random walks specifically on Euclidean lattices, advancing theoretical understanding.

Findings

Critical density is at most one for Euclidean lattices

Provides a theoretical upper bound for phase transition analysis

Enhances understanding of activated random walks behavior

Abstract

We show the critical density for activated random walks on Euclidean lattices is at most one.