Quenched Central Limit Theorems for Random Walks in Random Scenery

Abstract

Random walks in random scenery are processes defined by Zn := n k=1 ωS k where S := (S k , k ≥ 0) is a random walk evolving in Z d and ω := (ωx, x ∈ Z d) is a sequence of i.i.d. real random variables. Under suitable assumptions on the random walk S and the random scenery ω, almost surely with respect to ω, the correctly renormalized sequence (Zn) n≥1 is proved to converge in distribution to a centered Gaussian law with explicit variance .

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