16 citations · 27 across the 6 of their papers we have counts for
6 papers · 1 filter
Quantitative convergence rates for reversible Markov chains via strong random times
Daniel C. Jerison
Let be a discrete time Markov chain on a general state space. It is well-known that if is aperiodic and satisfies a drift and minorization condition, then it conver…
The Dirichlet problem for orthodiagonal maps
Ori Gurel-Gurevich, Daniel C. Jerison, Asaf Nachmias
We prove that the discrete harmonic function corresponding to smooth Dirichlet boundary conditions on orthodiagonal maps, that is, plane graphs having quadrilateral faces with orth…
A combinatorial criterion for macroscopic circles in planar triangulations
Ori Gurel-Gurevich, Daniel C. Jerison, Asaf Nachmias
Given a finite simple triangulation, we estimate the sizes of circles in its circle packing in terms of Cannon's vertex extremal length. Our estimates provide control over the size…
Sandpiles on the square lattice
Bob Hough, Dan Jerison, Lionel Levine
We give a non-trivial upper bound for the critical density when stabilizing i.i.d. distributed sandpiles on the lattice . We also determine the asymptotic spectral ga…
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…
General mixing time bounds for finite Markov chains via the absolute spectral gap
Daniel Jerison
We prove an upper bound on the total variation mixing time of a finite Markov chain in terms of the absolute spectral gap and the number of elements in the state space. Unlike resu…