A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

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...

We consider random walks in a random environment of the type p0 + γξz, where p0 denotes the transition probabilities of a stationary random walk on Z, to nearest neighbors, and ξz is an i.i.d. random perturbation. We give an explicit expansion, for small γ, of the asymptotic speed of the random walk under the annealed law, up to order 2. As an application, we construct, in dimension d ≥ 2, a wa...