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5
votes
1answer
181 views

Duration and critical groups order in sandpile models and chip firing games

The famous chip firing game (which is closely related to sandpile models) goes like this: Place chips at the vertices of a graph. REPEATEDLY: If a vertex $v$ of degree $d_{v}$ has at least ...
4
votes
2answers
271 views

Sandpile group corresponding to Abelian group

How we can prove each finite Abelian group is the sandpile group for some graph ?
5
votes
0answers
133 views

Local structure in the stochastic sandpile model

Here's a question that came up at the recent AIM conference on chip-firing and generalizations. The stochastic sandpile model, I think originally due to Manna, is a stochastic process that (in one ...
3
votes
0answers
220 views

What is the graphical version of the circle parking story?

The classical parking function story is as follows: we have cars $v_1,\ldots,v_n$ who approach a line of spaces marked $0,\ldots,n-1$ in order. Each car $v_i$ has space preference $a_i$. A car will ...
31
votes
1answer
1k views

What is the sandpile torsor?

Let G be a finite undirected connected graph. A divisor on G is an element of the free abelian group Div(G) on the vertices of G (or an integer-valued function on the vertices.) Summing over all ...
7
votes
0answers
380 views

Abelian sandpile models

This question is about a popular probabilistic model on graphs studied in physics, mostly, for the standard lattice in ${\mathbb R}^n$ but also on other graphs (this model is of the same spirit as ...