{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,17]],"date-time":"2026-10-17T00:37:08Z","timestamp":1792197428493,"version":"4.4.0"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,2,1]],"date-time":"2016-02-01T00:00:00Z","timestamp":1454284800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Geom. Funct. Anal."],"published-print":{"date-parts":[[2016,2]]},"DOI":"10.1007\/s00039-016-0358-7","type":"journal-article","created":{"date-parts":[[2016,2,23]],"date-time":"2016-02-23T12:16:35Z","timestamp":1456229795000},"page":"306-336","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["Apollonian structure in the Abelian sandpile"],"prefix":"10.1007","volume":"26","author":[{"given":"Lionel","family":"Levine","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wesley","family":"Pegden","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Charles K.","family":"Smart","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2016,2,23]]},"reference":[{"key":"358_CR1","doi-asserted-by":"crossref","unstructured":"P. Bak, C. Tang and K. Wiesenfeld. Self-organized criticality: an explanation of the 1\/f noise. Physical Review Letters, 59 (1987), 381\u2013384. doi: 10.1103\/PhysRevLett.59.381 .","DOI":"10.1103\/PhysRevLett.59.381"},{"key":"358_CR2","doi-asserted-by":"crossref","unstructured":"S. Caracciolo, G. Paoletti and A. Sportiello. Conservation laws for strings in the Abelian sandpile model. Europhysics Letters, (6)90 (2010), 60003. arXiv:1002.3974 .","DOI":"10.1209\/0295-5075\/90\/60003"},{"key":"358_CR3","first-page":"1","volume-title":"Lecture Notes in Mathematics, Vol. 1660","author":"M. G. Crandall","year":"1997","unstructured":"Crandall M. G.: Viscosity solutions: a primer, Viscosity solutions and applications (Montecatini Terme, 1995). In: (eds) Lecture Notes in Mathematics, Vol. 1660, pp. 1\u201343. Springer, Berlin (1997)"},{"key":"358_CR4","doi-asserted-by":"crossref","unstructured":"M. G. Crandall, H. Ishii and P.-L. Lions. User\u2019s guide to viscosity solutions of second order partial differential equations. Bulletin of the American Mathematical Society (N.S.), (1)27 (1992), 1\u201367. doi: 10.1090\/S0273-0979-1992-00266-5 .","DOI":"10.1090\/S0273-0979-1992-00266-5"},{"issue":"14","key":"358_CR5","doi-asserted-by":"crossref","first-page":"1613","DOI":"10.1103\/PhysRevLett.64.1613","volume":"64","author":"D. Dhar","year":"1990","unstructured":"Dhar D.: Self-organized critical state of sandpile automaton models. Physical Review Letters 64(14), 1613\u20131616 (1990)","journal-title":"Physical Review Letters"},{"key":"358_CR6","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.physa.2006.04.004","volume":"369","author":"D. Dhar","year":"2006","unstructured":"Dhar D.: Theoretical studies of self-organized criticality. Physica A 369, 29\u201370 (2006)","journal-title":"Physica A"},{"key":"358_CR7","doi-asserted-by":"crossref","unstructured":"D. Dhar, T. Sadhu, and S. Chandra. Pattern formation in growing sandpiles. Europhysics Letters, (4)85 (2009). arXiv:0808.1732 .","DOI":"10.1209\/0295-5075\/85\/48002"},{"key":"358_CR8","unstructured":"P. Diaconis and W. Fulton. A growth model, a game, an algebra, Lagrange inversion, and characteristic classes. Rend. Sem. Mat. Univ. Politec. Torino, (1)49 (1991), 95\u2013119 [Commutative algebra and algebraic geometry, II (Italian) (Turin, 1990), (1993)]."},{"key":"358_CR9","doi-asserted-by":"crossref","unstructured":"A. Feyden Boer, R. Meester, and F. Redig. Stabilizability and percolation in the infinite volume sandpile model. Annals of Probability, (2)37 (2009), 654\u2013675. doi: 10.1214\/08-AOP415 . arXiv:0710.0939 .","DOI":"10.1214\/08-AOP415"},{"key":"358_CR10","doi-asserted-by":"crossref","unstructured":"A. Fey, L. Levine, and Y. Peres. Growth rates and explosions in sandpiles. Journal of Statistical Physics, (1\u20133)138 (2010), 143\u2013159. arXiv:0901.3805 .","DOI":"10.1007\/s10955-009-9899-6"},{"key":"358_CR11","unstructured":"L. Levine, W. Pegden, and C. Smart. The Apollonian structure of integer super-harmonic matrices (2013). arXiv:1309.3267 ."},{"issue":"8","key":"358_CR12","first-page":"976","volume":"57","author":"L. Levine","year":"2010","unstructured":"Levine L., Propp J.: What is \u2026 a sandpile?. Notices of the American Mathematical Society 57(8), 976\u2013979 (2010)","journal-title":"Notices of the American Mathematical Society"},{"key":"358_CR13","doi-asserted-by":"crossref","first-page":"3207","DOI":"10.1103\/PhysRevA.42.3207","volume":"42","author":"S. H. Liu","year":"1990","unstructured":"Liu S. H., Kaplan T., Gray L. J.: Geometry and dynamics of deterministic sand piles. Physical Review A 42, 3207\u20133212 (1990)","journal-title":"Physical Review A"},{"key":"358_CR14","doi-asserted-by":"crossref","unstructured":"S. Ostojic. Patterns formed by addition of grains to only one site of an Abelian sandpile. Physica A, (1\u20132)318 (2003), 187\u2013199. doi: 10.1016\/S0378-4371(02)01426-7 .","DOI":"10.1016\/S0378-4371(02)01426-7"},{"key":"358_CR15","doi-asserted-by":"crossref","unstructured":"G. Paoletti. Deterministic abelian sandpile models and patterns, Ph.D. Thesis, Universit\u00e0a de Pisa (2012). http:\/\/pcteserver.mi.infn.it\/~caraccio\/PhD\/Paoletti .","DOI":"10.1007\/978-3-319-01204-9_2"},{"key":"358_CR16","unstructured":"W. Pegden and C. Smart. Convergence of the Abelian sandpile. Duke Mathematical Journal (2016, to appear). arXiv:1105.0111 ."},{"key":"358_CR17","unstructured":"W. Pegden, Sandpile galleries (2012). http:\/\/www.math.cmu.edu\/~wes\/sandgallery.html ."},{"key":"358_CR18","doi-asserted-by":"crossref","unstructured":"F. Redig. Mathematical aspects of the abelian sandpile model. Les Houches lecture notes (2005). http:\/\/www.math.leidenuniv.nl\/~redig\/sandpilelectures .","DOI":"10.1016\/S0924-8099(06)80051-X"},{"key":"358_CR19","unstructured":"D. Rossin. Propri\u00e9t\u00e9es combinatoires de certaines familles dautomates cellulaires, Ph.D. Thesis, \u00c9cole Polytechnique (2000)."}],"container-title":["Geometric and Functional Analysis"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00039-016-0358-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00039-016-0358-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00039-016-0358-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,4]],"date-time":"2019-09-04T22:21:02Z","timestamp":1567635662000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00039-016-0358-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,2]]}},"alternative-id":["358"],"URL":"https:\/\/doi.org\/10.1007\/s00039-016-0358-7","relation":{},"ISSN":["1016-443X","1420-8970"],"issn-type":[{"value":"1016-443X","type":"print"},{"value":"1420-8970","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2]]}}}