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math.PR2019
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…
math.PR2019
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…
math.PR2019★ 4 cited
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…