Journal
ANNALS OF MATHEMATICS
Volume 186, Issue 1, Pages 1-67Publisher
Princeton Univ, Dept Mathematics
DOI: 10.4007/annals.2017.186.1.1
Keywords
sandpile; circle packing; superharmonic; Apollonian
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Funding
- NSF [DMS-1004696, DMS-1004595, DMS-1243606]
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We prove that the set of quadratic growths attainable by integer-valued superharmonic functions on the lattice Z(2) has the structure of an Apollonian circle packing. This completely characterizes the PDE that determines the continuum scaling limit of the Abelian sandpile on the lattice Z(2).
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