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- W2110650571 abstract "We study the stationary distribution of the standard Abelian sandpile model in the box Λn = [-n, n] d ∩ ℤ d for d≥ 2. We show that as n→ ∞, the finite volume stationary distributions weakly converge to a translation invariant measure on allowed sandpile configurations in ℤ d . This allows us to define infinite volume versions of the avalanche-size distribution and related quantities. The proof is based on a mapping of the sandpile model to the uniform spanning tree due to Majumdar and Dhar, and the existence of the wired uniform spanning forest measure on ℤ d . In the case d > 4, we also make use of Wilson’s method." @default.
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- W2110650571 date "2004-04-09" @default.
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- W2110650571 title "Infinite Volume Limit for the Stationary Distribution of Abelian Sandpile Models" @default.
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- W2110650571 doi "https://doi.org/10.1007/s00220-004-1080-0" @default.
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