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.
