Uniform threshold for fixation of the stochastic sandpile model on the line

Abstract

We consider the abelian stochastic sandpile model. In this model, a site is deemed unstable when it contains more than one particle. Each unstable site, independently, is toppled at rate $1$, sending two of its particles to neighbouring sites chosen independently. We show that when the initial average density is less than $1/2$, the system locally fixates almost surely. We achieve this bound by analysing the parity of the total number of times each site is visited by a large number of particles under the sandpile dynamics.

arXiv comment21 pages including bibliography, 19 without

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Cited by in corpus (1)

• Dynamic correlations in the conserved Manna sandpile