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Uniform Threshold for Fixation of the Stochastic Sandpile Model on the Line

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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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Authors and Affiliations

  1. Indian Institute of Science Education Research Pune, Pune, Maharashtra, India

    Moumanti Podder

  2. Department of Statistics, University of Warwick, Warwick, Coventry, UK

    Leonardo T. Rolla

Authors
  1. Moumanti Podder
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  2. Leonardo T. Rolla
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Correspondence to Moumanti Podder.

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Communicated by Stefano Olla.

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Podder, M., Rolla, L.T. Uniform Threshold for Fixation of the Stochastic Sandpile Model on the Line. J Stat Phys 182, 52 (2021). https://doi.org/10.1007/s10955-021-02731-3

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