Asymptotic Height Distribution in High-Dimensional Sandpiles

Antal A. Járai () and Minwei Sun ()
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Antal A. Járai: University of Bath
Minwei Sun: University of Bath

Journal of Theoretical Probability, 2021, vol. 34, issue 1, 349-362

Abstract: Abstract We give an asymptotic formula for the single-site height distribution of Abelian sandpiles on $$\mathbb {Z}^d$$ Z d as $$d \rightarrow \infty $$ d → ∞ , in terms of $$\mathsf {Poisson}(1)$$ Poisson ( 1 ) probabilities. We provide error estimates.

Keywords: Abelian sandpile; Uniform spanning forest; Wilson’s method; Loop-erased random walk; Primary 60K35; Secondary 82C20 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-019-00962-5

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