Corpus ID: 115179036

Existence and uniqueness of the stationary measure in the continuous Abelian sandpile

  title={Existence and uniqueness of the stationary measure in the continuous Abelian sandpile},
  author={Wouter Kager and Haiyan Liu and Ronald W. J. Meester},
  journal={arXiv: Probability},
Let \Lambda be a finite subset of Z^d. We study the following sandpile model on \Lambda. The height at any given vertex x of \Lambda is a positive real number, and additions are uniformly distributed on some interval [a,b], which is a subset of [0,1]. The threshold value is 1; when the height at a given vertex exceeds 1, it topples, that is, its height is reduced by 1, and the heights of all its neighbours in \Lambda increase by 1/2d. We first establish that the uniform measure \mu on the so… Expand
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