We introduce random towers to study almost sure rates of correlation decay for partially hyperbolic attractors. Using this framework, we obtain abstract results on exponential, stretched exponential and polynomial rates. then apply our small perturbations Axiom A attractors, derived from Anosov systems solenoidal attractors with intermittency.

This paper introduces a stochastic, hybrid algorithm for global almost sure synchronization of two agents evolving on the circle. Recent results on stochastic hybrid systems are exploited and a Lyapunov-based proof of global almost sure synchronization is obtained. The same arguments establish that global almost sure practical synchronization is achieved in the presence of sufficiently small di...

We study the random walk in random environment on Z+ = {0, 1, 2, . . .}, where the environment is subject to a vanishing (random) perturbation. The two particular cases that we consider are: (i) random walk in random environment perturbed from Sinai’s regime; (ii) simple random walk with random perturbation. We give almost sure results on how far the random walker is from the origin, for almost...