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arXiv · 2001.04268

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

Moumanti Podder·Leonardo T. Rolla
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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.

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Moumanti Podder, Leonardo T. Rolla. 2020-01-13. Uniform threshold for fixation of the stochastic sandpile model on the line. https://doi.org/10.1007/s10955-021-02731-3

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