149 citations · 841 across the 44 of their papers we have counts for
57 papers
Universality Conjectures for Activated Random Walk
Lionel Levine, Vittoria Silvestri
Activated Random Walk is a particle system displaying Self-Organized Criticality, in that the dynamics spontaneously drive the system to a critical state. How universal is this cri…
Exact sampling and fast mixing of Activated Random Walk
Lionel Levine, Feng Liang
Activated Random Walk (ARW) is an interacting particle system on the -dimensional lattice . On a finite subset it defines a Markov chain o…
Branching in a Markovian Environment
Lila Greco, Lionel Levine
A branching process in a Markovian environment consists of an irreducible Markov chain on a set of "environments" together with an offspring distribution for each environment. At e…
How far do Activated Random Walkers spread from a single source?
Lionel Levine, Vittoria Silvestri
Unlike many particle systems, Activated Random Walk has nontrivial behavior even in one spatial dimension. We prove inner and outer bounds on the spread of n activated random walke…
The devil's staircase for chip-firing on random graphs and on graphons
Viktor Kiss, Lionel Levine, Lilla Tóthmérész
We study the behavior of the activity of the parallel chip-firing upon increasing the number of chips on an Erdős--Rényi random graph. We show that in various situations the result…
Solution manifold and Its Statistical Applications
Yen-Chi Chen
A solution manifold is the collection of points in a -dimensional space satisfying a system of equations with . Solution manifolds occur in several statistical problems…