Pierre Andreoletti

Alternative proof for the localization of Sinai's walk

We give an alternative proof of the localization of Sinai’s random walk in random environment under weaker hypothesis than the ones used by Sinai. Moreover, we give estimates that are stronger than the one of Sinai on the localization neighborhood and on the probability for the random walk to stay inside this neighborhood.

A Limit Result for a System of Particles in Random Environment

We consider an infinite system of particles in one dimension, each particle performs independent Sinai’s random walk in random environment. Considering an instant t, large enough, we prove a result in probability showing that the particles are trapped in the neighborhood of well defined points of the lattice depending on the random environment, t and the starting points of the particles.