The purpose of this book is to present systematically all known mathematical results on
Gibbs measures on Cayley trees (Bethe lattices). The Gibbs measure is a probability …

We review the status of the two-dimensional Abelian sandpile model as a strong candidate
to provide a lattice realization of logarithmic conformal invariance with a central charge c …

The Abelian sandpile process evolves configurations of chips on the integer lattice by
toppling any vertex with at least 4 chips, distributing one of its chips to each of its 4 …

We study dynamic correlations for current and mass, as well as the associated power
spectra, in the one-dimensional conserved Manna sandpile. We show that, in the …

Absorbing-state phase transition for driven-dissipative stochastic dynamics on Z Page 1 Invent
math (2012) 188:127–150 DOI 10.1007/s00222-011-0344-5 Absorbing-state phase transition …

We present simulations of the one-dimensional Oslo rice pile model in which the critical
height at each site is randomly reset after each toppling. We use the fact that the stationary …

We study the dynamics of two conservative lattice gas models on the infinite d-dimensional
hypercubic lattice: the Activated Random Walks (ARW) and the Stochastic Sandpiles Model …

This survey is an extended version of lectures given at the Cornell Probability Summer
School 2013. The fundamental facts about the Abelian sandpile model on a finite graph and …

Steady plastic flows have been compared to developed turbulence because the two
phenomena share the inherent complexity of particle trajectories, the scale free spatial …

The stochastic sandpile model (SSM) is a generalisation of the standard Abelian sandpile
model (ASM), in which topplings of unstable vertices are made random. When unstable, a …