86 citations · 218 across the 38 of their papers we have counts for
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Stability of patterns in the Abelian sandpile
Wesley Pegden, Charles K Smart
We show that the patterns in the Abelian sandpile are stable. The proof combines the structure theory for the patterns with the regularity machinery for non-divergence form ellipti…
The Apollonian structure of integer superharmonic matrices
Lionel Levine, Wesley Pegden, Charles K. Smart
We prove that the set of quadratic growths attainable by integer-valued superharmonic functions on the lattice has the structure of an Apollonian circle packing. Thi…
Apollonian structure in the Abelian sandpile
Lionel Levine, Wesley Pegden, Charles K. Smart
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 nei…
Convergence of the Abelian sandpile
Wesley Pegden, Charles K. Smart
The Abelian sandpile growth model is a diffusion process for configurations of chips placed on vertices of the integer lattice , in which sites with at least 2d chips…