Description
The stochastic sandpile model (SSM) is a generalisation of the standard Abelian sandpile model (ASM), in which topplings of unstable vertices are made random. When unstable, a vertex sends one grain to each of its neighbours independently with probability p ∈ (0,1). We study the SSM on complete graphs. Our main result is a combinatorial description of the recurrent states of the model, i.e. those that appear infinitely often in its longtime running. We show that these are given by convex sums of recurrent states for the ASM. This allows us to recover a wellknown result: that the number of integer lattice points in the ndimensional permutation polytope is equal to the number of labeled spanning forests on n vertices. We also study a family of socalled partial SSMs, in which some vertices topple randomly, while others topple deterministically (as in the ASM, sending one grain to all neighbours). We show that this distinction is meaningful, yielding sets of recurrent states that are in general different from those of both the ASM and SSM. We also show that to get all recurrent states of the SSM, we can allow up to two vertices to topple deterministically.Period  20 Sept 2024 

Event title  The 11th National Combinatorics and Graph Theory Conference 
Event type  Conference 
Conference number  11 
Location  Qingdao, ChinaShow on map 
Degree of Recognition  National 
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The 11th National Combinatorics and Graph Theory Conference
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