MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Upper Bound for the Critical Density of Biased Activated Random Walk

Lorenzo Taggi


We provide a new upper bound for the critical density of Activated Random Walk in case of biased distribution of jumps. With finite sleeping rate the bound is strictly less than one in one dimension for all initial particles distribution and in higher dimension for some initial particles distributions. This answers a question from Dickman, Rolla and Sidoravicius (2010) in case of bias.

MSC Codes:
82C22, 82C26
Activated Random Walk, Out-of-Equilibrium Phase Transition, Interacting Particle System

Related publications

2016 Journal Open Access
Lorenzo Taggi

Absorbing-state phase transition in biased activated random walk

In: Electronic journal of probability, 21 (2016), p. 13