In 1988, Bak, Tang and Wiesenfeld (BTW) introduced a lattice model of what they called “self-
organized criticality”. Since its appearance, this model has been studied intensively, both in …

We prove that the wired uniform spanning forest exhibits mean-field behaviour on a very
large class of graphs, including every transitive graph of at least quintic volume growth and …

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 …

Laplacian growth is the study of interfaces that move in proportion to harmonic measure.
Physically, it arises in fluid flow and electrical problems involving a moving boundary. We …

A popular theory of self-organized criticality relates driven dissipative systems to systems
with conservation. This theory predicts that the stationary density of the Abelian sandpile …

Consider the Abelian sandpile measure on Z^d, d≥2, obtained as the L→∞ limit of the
stationary distribution of the sandpile on -L,L^d∩Z^d. When adding a grain of sand at the …

We investigate the identity element of the sandpile group on finite approximations of the
Sierpinski gasket with normal boundary conditions and show that the sequence of piecewise …

Abstract 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 …

We compute the precise logarithmic corrections to mean-field scaling for various quantities
describing the uniform spanning tree of the four-dimensional hypercubic lattice Z 4. We are …

Bak, Tang, and Wiesenfeld introduced self-organized criticality with the example of a
growing sandpile that reaches then sustains a critical density. They presented the abelian …