210 citations · 786 across the 46 of their papers we have counts for
Showing 1998 · math.PRShow all
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math.PR1998
Indistinguishability of Percolation Clusters
Russell Lyons, Oded Schramm
We show that when percolation produces infinitely many infinite clusters on a Cayley graph, one cannot distinguish the clusters from each other by any invariantly defined property.…
math.PR1998★ 49 cited
Percolation Perturbations in Potential Theory and Random Walks
Itai Benjamini, Russell Lyons, Oded Schramm
We show that on a Cayley graph of a nonamenable group, almost surely the infinite clusters of Bernoulli percolation are transient for simple random walk, that simple random walk on…
math.PR1998★ 1 cited
A Simple Path to Biggins' Martingale Convergence for Branching Random Walk
Russell Lyons
We give a simple non-analytic proof of Biggins' theorem on martingale convergence for branching random walks.