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math.AP2021★ 1 cited
Integer superharmonic matrices on the -lattice
Ahmed Bou-Rabee
We prove that the set of quadratic growths achievable by integer superharmonic functions on the -lattice, a periodic subgraph of the square lattice with oriented edges, has the…
math.PR2021
Hamilton-Jacobi scaling limits of Pareto peeling in 2D
Ahmed Bou-Rabee, Peter S. Morfe
Pareto hull peeling is a discrete algorithm, generalizing convex hull peeling, for sorting points in Euclidean space. We prove that Pareto peeling of a random point set in two dime…
math.PR2021★ 1 cited
A shape theorem for exploding sandpiles
Ahmed Bou-Rabee
We study scaling limits of exploding Abelian sandpiles using ideas from percolation and front propagation in random media. We establish sufficient conditions under which a limit sh…