Limit theorems for random walks in random sceneries and related models

Random walks in random sceneries (RWRS) have been first studied by Borodin, Kesten and Spitzer, and Bolthausen. We will present the historical results, as well as the most recent ones completing and detailing the former. We will also be interested in a model introduced by Matheron and de Marsily to describe the trajectory of a particle in an inhomogeneous stratified medium, which consists in a type of random walk in Z^2 with random orientation of the horizontal lines. We will see how this model is related to RWRS. We will also present a natural extension of RWRS: the U-statistics indexed by random walks. Finally, we will present a model of a one dimensional random walk on the line with randomly located roundabouts. These results have been obtained in collaboration with Fabienne Castell, Nadine Guillotin-Plantard and Bruno Schapira (RWRS and Matheron-de Marsily's model); Brice Franke and Martin Wendler (U-statistics indexed by random walks); Alessandra Bianchi and Marco Lenci (random roundabouts).