On random walks and switched random walks 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...

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...

Random Walks on Random Graphs

The aim of this article is to discuss some of the notions and applications of random walks on finite graphs, especially as they apply to random graphs. In this section we give some basic definitions, in Section 2 we review applications of random walks in computer science, and in Section 3 we focus on walks in random graphs. Given a graphG = (V,E), let dG(v) denote the degree of vertex v for all...

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...