Daniel C. Jerison
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View article: Mixing time and eigenvalues of the abelian sandpile Markov chain
Mixing time and eigenvalues of the abelian sandpile Markov chain Open
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 (nonreversible) random walk on an abelian group, we give a formula for its…
View article: Quantitative convergence rates for reversible Markov chains via strong random times
Quantitative convergence rates for reversible Markov chains via strong random times Open
Let $(X_t)$ be a discrete time Markov chain on a general state space. It is well-known that if $(X_t)$ is aperiodic and satisfies a drift and minorization condition, then it converges to its stationary distribution $π$ at an exponential ra…
View article: A combinatorial criterion for macroscopic circles in planar triangulations
A combinatorial criterion for macroscopic circles in planar triangulations Open
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 of the largest circle in the packing. We use them, combine…