149 citations · 841 across the 44 of their papers we have counts for
5 papers · 1 filter
Internal DLA for cylinders
David Jerison, Lionel Levine, Scott Sheffield
We show that space-time averages of the fluctuations of internal DLA on a cylinder Z_N x Z converge in law to the Gaussian free field.
Abelian networks I. Foundations and examples
Benjamin Bond, Lionel Levine
In Deepak Dhar's model of abelian distributed processors, automata occupy the vertices of a graph and communicate via the edges. We show that two simple axioms ensure that the fina…
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…
How to decompose a permutation into a pair of labeled Dyck paths by playing a game
Louis J. Billera, Lionel Levine, Karola Meszaros
We give a bijection between permutations of length 2n and certain pairs of Dyck paths with labels on the down steps. The bijection arises from a game in which two players alternate…
Escape rates for rotor walk in Z^d
Laura Florescu, Shirshendu Ganguly, Lionel Levine +1
Rotor walk is a deterministic analogue of random walk. We study its recurrence and transience properties on Z^d for the initial configuration of all rotors aligned. If n particles…