Étude de la marche aléatoire biaisée en milieu aléatoire
The main goal of this Master thesis is to provide an introduction to the random walks in random environments (RWRE). This is a vast domain, our interest will be on models where the walk is directionnally transient in order to study asymptotical behavior. We will present severals models and associated mains results. We will see some basic techniques used in this field. One of the tools that has made the most progress is the renewal structure which allows us to answer questions about the speed of the biased random walk. This is the subject of this thesis, we deal with the following question : Is the speed of the biaised random walk on a Galton-Watson tree monotonous with respect to the environnement ? We answer in the affirmative for a high bias.
Random walk in random environment (RWRE) Galton-Watson tree Velocity of the biased random walk in random environment Renewal structure