2021/10/14 by Bou-Rabee, Ahmed
#Analysis of PDEs (math.AP) #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)
paper · doi:10.48550/arxiv.2110.07556
We prove that the set of quadratic growths achievable by integer superharmonic functions on the F-lattice, a periodic subgraph of the square lattice with oriented edges, has the structure of an overlapping circle packing. The proof recursively constructs a distinct pair of recurrent functions for each rational point on a hyperbola. This proves a conjecture of Smart (2013) and completely describes the scaling limit of the Abelian sandpile on the F-lattice.