Geodesic
The Apollonian structure of integer superharmonic matrices
Lionel Levine1 ; Wesley Pegden2 ; Charles K. Smart3
1 Cornell University, Ithaca, NY
2 Carnegie Mellon University, Pittsburgh, PA
3 The University of Chicago, Chicago, IL
Annals of mathematics, Tome 186 (2017) no. 1, pp. 1-67.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove that the set of quadratic growths attainable by integer-valued superharmonic functions on the lattice $\mathbb{Z}^2$ 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 $\mathbb{Z}^2$.
DOI : 10.4007/annals.2017.186.1.1

Lionel Levine 1 ; Wesley Pegden 2 ; Charles K. Smart 3

1 Cornell University, Ithaca, NY
2 Carnegie Mellon University, Pittsburgh, PA
3 The University of Chicago, Chicago, IL 
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Lionel Levine; Wesley Pegden; Charles K. Smart. The Apollonian structure of integer superharmonic matrices. Annals of mathematics, Tome 186 (2017) no. 1, pp. 1-67. doi : 10.4007/annals.2017.186.1.1. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.186.1.1/

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