53 citations · 55 across the 3 of their papers we have counts for
6 papers
Positional Voting and Doubly Stochastic Matrices
Jacqueline Anderson, Brian Camara, John Pike
We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a…
Double jump phase transition in a soliton cellular automaton
Lionel Levine, Hanbaek Lyu, John Pike
In this paper, we consider the soliton cellular automaton introduced in [Takahashi 1990] with a random initial configuration. We give multiple constructions of a Young diagram desc…
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…
Poisson statistics of eigenvalues in the hierarchical Dyson model
Alexander Bendikov, Anton Braverman, John Pike
Let be a locally compact separable ultrametric space. Given a measure on and a function defined on the set of all balls we consider t…
A note on the Poincaré and Cheeger inequalities for simple random walk on a connected graph
John Pike
In 1991, Persi Diaconis and Daniel Stroock obtained two canonical path bounds on the second largest eigenvalue for simple random walk on a connected graph, the Poincaré and Cheeger…
Stein's method and the Laplace distribution
John Pike, Haining Ren
Using Stein's method techniques, we develop a framework which allows one to bound the error terms arising from approximation by the Laplace distribution and apply it to the study o…