Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have