149 citations · 841 across the 44 of their papers we have counts for
6 papers · 1 filter
Mixing time and eigenvalues of the abelian sandpile Markov chain
Daniel C. Jerison, Lionel Levine, John Pike
The abelian sandpile model defines a Markov chain whose states are integer-valued functions on the vertices of a simple connected graph . By viewing this chain as a (nonreversib…
Abelian logic gates
Alexander E. Holroyd, Lionel Levine, Peter Winkler
An abelian processor is an automaton whose output is independent of the order of its inputs. Bond and Levine have proved that a network of abelian processors performs the same comp…
Multi-Eulerian tours of directed graphs
Matthew Farrell, Lionel Levine
Not every graph has an Eulerian tour. But every finite, strongly connected graph has a multi-Eulerian tour, which we define as a closed path that uses each directed edge at least o…
CoEulerian graphs
Matthew Farrell, Lionel Levine
We suggest a measure of "Eulerianness" of a finite directed graph and define a class of "coEulerian" graphs. These are the graphs whose Laplacian lattice is as large as possible. A…
Formation of an interface by competitive erosion
Shirshendu Ganguly, Lionel Levine, Yuval Peres +1
In 2006, the fourth author proposed a graph-theoretic model of interface dynamics called competitive erosion. Each vertex of the graph is occupied by a particle that can be either…
The divisible sandpile at critical density
Lionel Levine, Mathav Murugan, Yuval Peres +1
The divisible sandpile starts with i.i.d. random variables ("masses") at the vertices of an infinite, vertex-transitive graph, and redistributes mass by a local toppling rule in an…