Density conjecture for the square-grid sandpile

From papers

Let b6cb6_c be the threshold density of the fixed-energy sandpile on the square grid, and let b6sb6_s be the stationary density of the classical abelian sandpile on b62b6^2. Density conjecture. On the square grid,

b6c=17/8.b6_c=17/8.

This prediction says that driving and dissipation in the classical model push it toward the critical density of the fixed-energy model. The value 17/817/8 is the rigorously estimated stationary density, while the equality with the fixed-energy threshold remains open.

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Sources & referencesView supporting material

Primary source

Anne Fey, Lionel Levine and David B. Wilson, “The approach to criticality in sandpiles”, arXiv:1001.3401 (2010).

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