The Apollonian structure of integer superharmonic matrices
Analysis of PDEs
2017-07-18 v4 Number Theory
Probability
Abstract
We prove that the set of quadratic growths attainable by integer-valued superharmonic functions on the lattice has the structure of an Apollonian circle packing. This completely characterizes the PDE which determines the continuum scaling limit of the Abelian sandpile on the lattice .
Cite
@article{arxiv.1309.3267,
title = {The Apollonian structure of integer superharmonic matrices},
author = {Lionel Levine and Wesley Pegden and Charles K. Smart},
journal= {arXiv preprint arXiv:1309.3267},
year = {2017}
}
Comments
56 pages, many figures. Typo in T1.1 corrected (2 -> 0)