374 citations · 1.8k across the 64 of their papers we have counts for
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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
Noise Sensitivity of Boolean Functions and Applications to Percolation
Itai Benjamini, Gil Kalai, Oded Schramm
It is shown that a large class of events in a product probability space are highly sensitive to noise, in the sense that with high probability, the configuration with an arbitrary…
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…