OpenYear of origin: 1987
Posted online: 2018-10-23 19:53:11Z by Henrik Shahgholian
Cite as: P-181023.1
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Abelian Sandpile Model (ASM) is a lattice growth model for configurations of chips distributed on vertices of $\mathbb Z^d$. A vertex carrying at least $2d$ chips topples giving a single chip to all its $2d$ lattice neighbours, and losing $2d$ chips itself. If there are no sites with more than $2d-1$ chips, the process terminates. For any finite non-negative initial configuration of chips, subsequently toppling all sites with at least $2d$ chips, the process terminates in finite steps. This process is abelian in the sense that the final configuration of chips is independent of the order of toppling. The model originates in the work of Bak-Tang-Wiesenfeld [bak1987self].
As the number of particles tend to infinity the ASM has a uniques scaling limit which tends to a free boundary problems with facets. See [pegden2013convergence].
Problem: Is the scaling limit of ASM convex?
No solutions added yet