# Questions tagged [sandpile]

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### Measuring the failure of basepoint independence of the rotor-routing model for non-planar ribbon graphs

In this question from 2012, Jordan Ellenberg asks if the set of spanning trees of a graph $G$ is naturally a torsor for the critical group (also called the sandpile group or the picard group $Pic^0(G)$...
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### Strange formula in arithmetic dynamic

Added: another function like that is $S_p f(z) = f(z)+\frac{f(\sqrt{zp})^2}{f(p)}$ in a field of characteristic two. We discovered the following operator which acts on the space of polynomials (or ...
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### How is the Jacobian or Sandpile group of a graph computed?

From what I understand, given a graph, the Jacobian group and the Sandpile group refer to the same object. Until now, I have been computing this group in the way detailed in Chapter 1 of this ...
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### Probabilistic distribution of sandpile model type

Let $G=(V,E)$ be a connected graph. Assume that $m\leqslant |V|$ hedgehogs sit in the vertices of $G$. If there are $r\geqslant 2$ hedgehogs in the same vertex $v\in V$, one of them goes to a randomly ...
288 views

### power laws emerging from the sandpile model

Is there a rigorous proof that the abelian sandpile model generates a power law distribution of avalanche lengths?
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### Sandpile group corresponding to Abelian group

How we can prove each finite Abelian group is the sandpile group for some graph ?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Why is the identity element of the sandpile group self-similar?

I've been reading about the Abelian Sandpile Model and noticed the identity element of the sandpile group on the square has self-similar components. The sandpile group of the 198x198 square of ...
Given a connected graph $G$, two players, Blue and Green, play the following game: initially, all vertices are unclaimed. Players alternate turns. On her turn, Blue adds a token to either an ...
Does anyone know of any work on the following model or variants thereof?: Finitely many chips are distributed on the integers at time 0. To find the distribution at time $t+1$, take all the chips at ...