Marche aléatoire dynamique dans une scène aléatoire

Abstract

In this Note, we consider a ℤ-random walk ( S n ) n∈ℕ on nearest neighbours with dynamical transition probabilities determined by a quasiperiodic function, in a random scenery ξ(α),α ε ℤ, a family of i.i.d. random variables, independent of the random walk. First we prove that a local limit theorem holds for ( S n ) n∈ℕ which is recurrent on its moving average. Next, we show explicitly, that Z n = ∑ t=0 n ξ( S i ) satisfies a law of large numbers.