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The main contribution of this paper is the development of a novel approach to multi-scale analysis that we believe can be used to analyse processes with non-equilibrium dynamics. Our approach will be referred to as...

The main contribution of this paper is the development of a novel approach to multi-scale analysis that we believe can be used to analyse processes with non-equilibrium dynamics. Our approach will be referred to as...

Let (G,μ) be a uniformly elliptic random conductance graph on Z ^d with a Poisson point process of particles at time t=0 that perform independent simple random walks. We show that inside a cube Q _K of...

In this article, we study the existence of an absorbing-state phase transition of an Abelian process that generalises the Activated Random Walk (ARW). Given a vertex transitive G = (V;E), we associate to each site x 2 V a...

We consider the activated random walk model on general vertextransitive graphs. A central question in this model is whether the critical density μ _c for sustained activity is strictly between 0 and 1. It was known...

We introduce a two-type first passage percolation competition model on infinite connected graphs as follows. Type 1 spreads through the edges of the graph at rate 1 from a single distinguished site, while all other sites are...

Consider the model where nodes are initially distributed as a Poisson point process with intensity λ over Rd and are moving in continuous time according to independent Brownian motions. We assume that nodes are capable of...