-- Markov chains indexed by trees-- (2008)
25th January 2005 1 Introduction In the study of Markov chains indexed by trees, one lets time be the vertices of a tree, instead of the the integers. This generalization leads to a number of more or...
Visibility to infinity in the hyperbolic plane, despite obstacles (2008)
Benjamini, Itai, Jonasson, Johan, Schramm, Oded, Tykesson, Johan
Suppose that $Z$ is a random closed subset of the hyperbolic plane $\H^2$, whose law is invariant under isometries of $\H^2$. We prove that if the probability that $Z$ contains a fixed ball of radius...
Continuum percolation at and above the uniqueness treshold on homogeneous spaces (2007)
We consider the Poisson Boolean model of continuum percolation on a homogeneous Riemannian manifold $M$. Let $lambda$ be intensity of the Poisson process in the model and let $lambda_u$ be the...
The number of unbounded components in the Poisson Boolean model in hyperbolic space (2006)
We consider the Poisson Boolean continuum percolation model in n-dimensional hyperbolic space. In 2 dimensions we show that there are intensities for the underlying Poisson process for which there...