Séminaire des doctorants

A (random) walk in random environment

by Alexandre Legrand


Random walks are essential processes from probability theory, as they appear in many natural problems. In this talk, we are interested in the behavior of a random walk in an inhomogeneous space, which we call the "environment". We consider the case of a 1D random walk, and focus on some of its most basic properties, more precisely the Law of Large Numbers and the question of Recurrence/Transience; and we see that, even in this simple case, the addition of inhomogeneities in the space may generate behaviors very different from that of the homogeneous process.