Self-organized criticality (SOC) maintains that complex behavior can develop spontaneously
in certain multi-body systems whose dynamics vary abruptly. This is a clear and concise …

This is an invited survey on the relation between the partition function of the Potts model and
the Tutte polynomial. On the assumption that the Potts model is more familiar we have …

A variant of the chip-firing game on a graph is defined. It is shown that the set of
configurations that are stable and recurrent for this game can be given the structure of an …

The collective behavior of interconnected spiking nerve cells is investigated. It is shown that
a variety of model systems exhibit the same short-time behavior and rapidly converge to …

For a graph $ G $, we construct two algebras whose dimensions are both equal to the
number of spanning trees of $ G $. One of these algebras is the quotient of the polynomial …

The group of recurrent configurations in the sandpile model, introduced by Dhar, may be
considered as a finite abelian group associated with any graph G; we call it the sandpile …

Driven systems of interconnected blocks with stick-slip friction capture main features of
earthquake processes. The microscopic dynamics closely resemble those of spiking nerve …

In this survey of graph polynomials, we emphasize the Tutte polynomial and a selection of
closely related graph polynomials such as the chromatic, flow, reliability, and shelling …

We study the interplay between chip-firing games and potential theory on graphs,
characterizing reduced divisors (G-parking functions) on graphs as the solution to an energy …

We determine the distribution of the sandpile group (or Jacobian) of the Erdős-Rényi
random graph $ G (n, q) $ as $ n $ goes to infinity. We prove the distribution converges to a …