210 citations · 786 across the 46 of their papers we have counts for
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math.PR2001★ 20 cited
Markov Chain Intersections and the Loop-Erased Walk
Russell Lyons, Yuval Peres, Oded Schramm
Let X and Y be independent transient Markov chains on the same state space that have the same transition probabilities. Let L denote the ``loop-erased path'' obtained from the path…
math.PR2001★ 18 cited
Coupling and Bernoullicity in random-cluster and Potts models
Olle Haggstrom, Johan Jonasson, Russell Lyons
An explicit coupling construction of random-cluster measures is presented. As one of the applications of the construction, the Potts model on amenable Cayley graphs is shown to exh…
math.PR2001★ 1 cited
Change Intolerance in Spanning Forests
Deborah Heicklen, Russell Lyons
Call a percolation process on edges of a graph change intolerant if the status of each edge is almost surely determined by the status of the other edges. We give necessary and suff…