210 citations · 786 across the 46 of their papers we have counts for
Showing 1999Show all
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math.PR1999★ 5 cited
Singularity of Some Random Continued Fractions
Russell Lyons
We prove singularity of some distributions of random continued fractions that correspond to iterated function systems with overlap and a parabolic point. These arose while studying…
math.PR1999★ 82 cited
Phase Transitions on Nonamenable Graphs
Russell Lyons
We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive g…
math.PR1999★ 13 cited
Stationary Measures for Random Walks in a Random Environment with Random Scenery
Russell Lyons, Oded Schramm
Let act on a countable set V with only finitely many orbits. Given a -invariant random environment for a Markov chain on V and a random scenery, we exhibit, under certain co…