Frómeta, Susana; Jara, Milton Scaling limit for a long-range divisible sandpile. (English) Zbl 1430.60082 SIAM J. Math. Anal. 50, No. 3, 2317-2361 (2018). Cited in 2 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 31C20 Discrete potential theory 35R35 Free boundary problems for PDEs Keywords:divisible sandpile; Green’s functions; \(\alpha\)-stable laws; fractional Laplacian; obstacle problem PDF BibTeX XML Cite \textit{S. Frómeta} and \textit{M. Jara}, SIAM J. Math. Anal. 50, No. 3, 2317--2361 (2018; Zbl 1430.60082) Full Text: DOI arXiv References: [1] P. Bak, C. Tang, and K. Wiesenfeld, Self-organized criticality: An explanation of the \(1/f\) noise, Phys. Rev. Lett., 59 (1987), pp. 381–384. [2] L. Caffarelli, The obstacle problem revisited, J. Fourier Anal. Appl., 4 (1998), pp. 383–402. · Zbl 0928.49030 [3] L. Evans, Partial Differential Equations, Grad. Stud. Math., AMS, Providence, RI, 2010. · Zbl 1194.35001 [4] A. Friedman, Variational Principles and Free-Boundary Problems, Dover Books on Mathematics, Dover, Mineola, NY, 2010. [5] J.-F. L. Gall and J. Rosen, The range of stable random walks, Ann. Probab., 19 (1991), pp. 650–705. · Zbl 0729.60066 [6] G. Lawler, Intersections of Random Walks, Probab. Appl., Birkhäuser, Boston, 1996. · Zbl 0925.60078 [7] G. Lawler and V. Limic, Random Walk: A Modern Introduction, Cambridge Stud. Adv. Math., Cambridge University Press, Cambridge, 2010. · Zbl 1210.60002 [8] G. F. Lawler, M. Bramson, and D. Griffeath, Internal diffusion limited aggregation, Ann. Probab., 20 (1992), pp. 2117–2140. · Zbl 0762.60096 [9] L. Levine, W. Pegden, and C. K. Smart, Apollonian structure in the Abelian sandpile, Geom. Funct. Anal., 26 (2016), pp. 306–336. · Zbl 1341.60129 [10] L. Levine and Y. Peres, Strong spherical asymptotics for rotor-router aggregation and the divisible sandpile, Potential Anal., 30 (2009), pp. 1–27. · Zbl 1165.82309 [11] L. Levine and Y. Peres, Scaling limits for internal aggregation models with multiple sources, J. Anal. Math., 111 (2010), pp. 151–219. · Zbl 1210.82031 [12] C. Lucas, The limiting shape for drifted internal diffusion limited aggregation is a true heat ball, Probab. Theory Related Fields, 159 (2014), pp. 197–235. · Zbl 1296.60115 [13] W. Pegden and C. K. Smart, Convergence of the Abelian sandpile, Duke Math. J., 162 (2013), pp. 627–642. · Zbl 1283.60124 [14] T. Sadhu and D. Dhar, Pattern formation in fast-growing sandpiles, Phys. Rev. E (3), 85 (2012), 021107. [15] L. Silvestre, Regularity of the obstacle problem for a fractional power of the Laplace operator, Comm. Pure Appl. Math., 60 (2007), pp. 67–112. · Zbl 1141.49035 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.