3 research outputs found
A natural stochastic extension of the sandpile model on a graph
We introduce a new model of a stochastic sandpile on a graph containing a
sink. When unstable, a site sends one grain to each of its neighbours
independently with probability . For , this coincides with
the standard Abelian sandpile model. In general, for , the set of
recurrent configurations of this sandpile model is different from that of the
Abelian sandpile model. We give a characterisation of this set in terms of
orientations of the graph . We also define the lacking polynomial as
the generating function counting this set according to the number of grains,
and show that this polynomial satisfies a recurrence which resembles that of
the Tutte polynomial