• Corpus ID: 238857112

Integer superharmonic matrices on the $F$-lattice

  title={Integer superharmonic matrices on the \$F\$-lattice},
  author={Ahmed Bou-Rabee},
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. 


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