19 citations · 30 across the 5 of their papers we have counts for
5 papers · 1 filter
The Pile Process on a Cycle
Itai Benjamini, Eric Shellef
Consider a finite particle system in which, at each step, one particle from a vertex with a lower neighboring vertex moves to a neighboring vertex of minimum height. For the cycle…
On the range of a random walk in a torus and random interlacements
Eviatar B. Procaccia, Eric Shellef
Let a simple random walk run inside a torus of dimension three or higher for a number of steps which is a constant proportion of the volume. We examine geometric properties of the…
Nonfixation for Activated Random Walks
Eric Shellef
We consider the activated random walk (ARW) model where particles follow the path of a general Markov process on a general graph. We prove ARW dominates a simpler process, multiple…
An Upper Bound on the critical density for Activated Random Walks on Euclidean Lattices
Eric Shellef
We show the critical density for activated random walks on Euclidean lattices is at most one.
IDLA on the Supercritical Percolation Cluster
Eric Shellef
We consider the internal diffusion limited aggregation (IDLA) process on the infinite cluster in supercritical Bernoulli bond percolation on Euclidean lattices. It is shown that th…