Expanding measures: Random walks and rigidity on homogeneous spaces

Zariski Dense Random Walks on Homogeneous Spaces

Random Walks on Homogeneous Spaces and Diophantine Approximation on Fractals

We extend results of Y. Benoist and J.-F. Quint concerning random walks on homogeneous spaces of simple Lie groups to the case where the measure defining the random walk generates a semigroup which is not necessarily Zariski dense, but satisfies some expansion properties for the adjoint action. Using these dynamical results, we study Diophantine properties of typical points on some self-similar...

Recurrence and ergodicity of random walks on linear groups and on homogeneous spaces

We discuss recurrence and ergodicity properties of random walks and associated skew products for large classes of locally compact groups and homogeneous spaces. In particular we show that a closed subgroup of a product of finitely many linear groups over local fields supports a recurrent random walk if and only if it has at most quadratic growth. We give also a detailed analysis of ergodicity p...

Anisotropic Branching Random Walks on Homogeneous Trees

Symmetric branching random walk on a homogeneous tree exhibits a weak survival phase: For parameter values in a certain interval, the population survives forever with positive probability, but, with probability one, eventually vacates every finite subset of the tree. In this phase, particle trails must converge to the geometric boundary of the tree. The random subset 3 of the boundary consisti...

Homogeneous Superpixels from Random Walks

This paper presents a novel algorithm to generate homogeneous superpixels from the process of Markov random walks. We exploit Markov clustering (MCL) as the methodology, a generic graph clustering method based on stochastic flow circulation. In particular, we introduce a new graph pruning strategy called compact pruning in order to capture intrinsic local image structure, and thereby keep the s...