Some asymptotic properties of random walks on homogeneous spaces

Zariski Dense Random Walks on Homogeneous Spaces

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

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...

Asymptotic properties of coalescing random walks

A Coalescing random walk is an interacting particle system which can be described as the following. Suppose that there is one particle located at each integer position [0, n] at time point 0 and that a particle is chosen at random at any time point t among the remaining in [1, n] and moves one step in some direction, where the direction can be deterministic or stochastic. The particle coalesce ...

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...