2 citations · 3 across the 2 of their papers we have counts for
8 papers · 1 filter
Conceptual Proofs of L log L Criteria
Russell Lyons, Robin Pemantle, Yuval Peres
The Kesten-Stigum Theorem is a fundamental criterion for the rate of growth of a supercritical branching process, showing that an L log L condition is decisive. In critical and sub…
Random Walk in a Random Environment and First-Passage Percolation on Trees
Robin Pemantle, Russell Lyons
We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the…
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…
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…
Explicit isoperimetric constants and phase transitions in the random-cluster model
Olle Haggstrom, Johan Jonasson, Russell Lyons
The random-cluster model is a dependent percolation model that has applications in the study of Ising and Potts models. In this paper, several new results are obtained for the rand…
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…