Ballistic random walks in random environment as rough paths: convergence and area anomaly

Ballistic Random Walks in Random Environment at Low Disorder

We consider random walks in a random environment of the type p0 + γξz, where p0 denotes the transition probabilities of a stationary random walk on Z, to nearest neighbors, and ξz is an i.i.d. random perturbation. We give an explicit expansion, for small γ, of the asymptotic speed of the random walk under the annealed law, up to order 2. As an application, we construct, in dimension d ≥ 2, a wa...

Random Walks in Random Environment

Random Walks in Random Environment

My main research interest is in theoretical and applied probability mainly focusing on discrete problems arising out of combinatorics, statistical physics and computer science. In particular I am interested in random graphs, probability on tress, combinatorial optimization and statistical physics problems, recursive distributional equations, branching random walks, percolation theory, interacti...

Lattice paths and random walks

Lattice paths are ubiquitous in combinatorics and algorithmics, where they are either studied per se, or as a convenient encoding of other structures. Logically, they play an important role in Philippe’s papers. For instance, they are central in his combinatorial theory of continued fractions, to which Chapter 3 of this volume is devoted. In this chapter, we present a collection of seven papers...

Sharp ellipticity conditions for ballistic behavior of random walks in random environment