A natural stochastic extension of the sandpile model on a graph

Chan, Yao-ban, Marckert, Jean-François and Selig, Thomas (2013) A natural stochastic extension of the sandpile model on a graph. Journal of Combinatorial Theory, Series A, 120 7: 1913-1928. doi:10.1016/j.jcta.2013.07.004

Author Chan, Yao-ban
Marckert, Jean-François
Selig, Thomas
Title A natural stochastic extension of the sandpile model on a graph
Journal name Journal of Combinatorial Theory, Series A   Check publisher's open access policy
ISSN 0097-3165
Publication date 2013-07
Sub-type Article (original research)
DOI 10.1016/j.jcta.2013.07.004
Volume 120
Issue 7
Start page 1913
End page 1928
Total pages 16
Place of publication Maryland Heights, MO, United States
Publisher Academic Press
Collection year 2014
Language eng
Formatted abstract
We introduce a new model of a stochastic sandpile on a graph G containing a sink. When unstable, a site sends one grain to each of its neighbours independently with probability p ∈ (0,1). The case p = 1 coincides with the standard Abelian sandpile model. In general, for p ∈ (0,1), 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 G. We also define the lacking polynomial LG 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.
Keyword Random sandpile model
Tutte polynomial
Recurrent configurations
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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Created: Wed, 11 Sep 2013, 16:56:35 EST by Kay Mackie on behalf of School of Mathematics & Physics