Random walks on projective 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...

Sampling Combinatorial Spaces Using Biased Random Walks

For probabilistic reasoning, one often needs to sample from a combinatorial space. For example, one may need to sample uniformly from the space of all satisfying assignments. Can state-of-the-art search procedures for SAT be used to sample effectively from the space of all solutions? And, if so, how uniformly do they sample? Our initial results find that on the positive side, one can find all s...

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...

Random walk on random walks

In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density ρ ∈ (0,∞). At each step the random walk performs a nearest-neighbour jump, moving to the right with probability p◦ when it is on a vacant site and probability p• when it is on an oc...