dc.contributor.author | Levine, Lionel | |
dc.contributor.author | Pegden, Wesley | |
dc.contributor.author | Smart, Charles | |
dc.date.accessioned | 2017-02-16T19:07:29Z | |
dc.date.available | 2017-02-16T19:07:29Z | |
dc.date.issued | 2016-02 | |
dc.identifier.issn | 1016-443X | |
dc.identifier.issn | 1420-8970 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/106972 | |
dc.description.abstract | The 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.sponsorship | National Science Foundation (U.S.) (grants DMS-1004696, DMS-1004595 and DMS- 1243606) | en_US |
dc.publisher | Springer International Publishing | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1007/s00039-016-0358-7 | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | en_US |
dc.source | Springer International Publishing | en_US |
dc.title | Apollonian structure in the Abelian sandpile | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Levine, 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.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.mitauthor | Smart, Charles | |
dc.relation.journal | Geometric and Functional Analysis | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2016-08-18T15:40:26Z | |
dc.language.rfc3066 | en | |
dc.rights.holder | Springer International Publishing | |
dspace.orderedauthors | Levine, Lionel; Pegden, Wesley; Smart, Charles K. | en_US |
dspace.embargo.terms | N | en |
mit.license | OPEN_ACCESS_POLICY | en_US |
mit.metadata.status | Complete | |