The Apollonian structure of integer superharmonic matrices

• 成果类型: Article
• 署名作者: Levine, Lionel; Pegden, Wesley; Smart, Charles K.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2017.186.1.1
• 发表日期: 2017
• 页码: 1-67
• 关键词: abelian sandpile; circle packings

摘要

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).