Publications (60)
Uniform non-amenability, cost, and the first l^2-Betti number
Russell Lyons, Mikaël Pichot, Stéphane Vassout
It is shown that $2β_1(\G)\leq h(\G)$ for any countable group $\G$, where $β_1(\G)$ is the first -Betti number and $h(\G)$ the uniform isoperimetric constant. In particul…
Ideal Poisson-Voronoi tessellations on hyperbolic spaces
Matteo D'Achille, Nicolas Curien, Nathanaël Enriquez +2
We study the limit in low intensity of Poisson--Voronoi tessellations in hyperbolic spaces for . In contrast to the Euclidean setting, a limiting nontri…
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…
A calculus proof of the Cramér-Wold theorem
Russell Lyons, Kevin Zumbrun
We present a short, elementary proof not involving Fourier transforms of the theorem of Cramér and Wold that a Borel probability measure is determined by its values on half-spaces…
Hyperbolic Space Has Strong Negative Type
Russell Lyons
It is known that hyperbolic spaces have strict negative type, a condition on the distances of any finite subset of points. We show that they have strong negative type, a condition…
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…