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dc.contributor.authorLevine, Lionel
dc.contributor.authorPegden, Wesley
dc.contributor.authorSmart, Charles
dc.date.accessioned2017-02-16T19:07:29Z
dc.date.available2017-02-16T19:07:29Z
dc.date.issued2016-02
dc.identifier.issn1016-443X
dc.identifier.issn1420-8970
dc.identifier.urihttp://hdl.handle.net/1721.1/106972
dc.description.abstractThe Abelian sandpile process evolves configurations of chips on the integer lattice by toppling any vertex with at least 4 chips, distributing one of its chips to each of its 4 neighbors. When begun from a large stack of chips, the terminal state of the sandpile has a curious fractal structure which has remained unexplained. Using a characterization of the quadratic growths attainable by integer-superharmonic functions, we prove that the sandpile PDE recently shown to characterize the scaling limit of the sandpile admits certain fractal solutions, giving a precise mathematical perspective on the fractal nature of the sandpile.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (grants DMS-1004696, DMS-1004595 and DMS- 1243606)en_US
dc.publisherSpringer International Publishingen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00039-016-0358-7en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourceSpringer International Publishingen_US
dc.titleApollonian structure in the Abelian sandpileen_US
dc.typeArticleen_US
dc.identifier.citationLevine, Lionel, Wesley Pegden, and Charles K. Smart. “Apollonian Structure in the Abelian Sandpile.” Geometric and Functional Analysis 26, no. 1 (February 2016): 306–336.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorSmart, Charles
dc.relation.journalGeometric and Functional Analysisen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2016-08-18T15:40:26Z
dc.language.rfc3066en
dc.rights.holderSpringer International Publishing
dspace.orderedauthorsLevine, Lionel; Pegden, Wesley; Smart, Charles K.en_US
dspace.embargo.termsNen
mit.licenseOPEN_ACCESS_POLICYen_US
mit.metadata.statusComplete


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