Quenched Central Limit Theorems for Random Walks in Random Scenery

Abstract

Random walks in random scenery are processes defined by $$Z_n:=\sum _{k=1}^n{\omega }_{S_k}$$ where $S:=(S_k,k\ge 0)$ is a random walk evolving in ${\mathbb{Z}}^d$ and $\omega :=({\omega }_x,x\in {\mathbb{Z}}^d)$ is a sequence of i.i.d. real random variables. Under suitable assumptions on the random walk $S$ and the random scenery $\omega$, almost surely with respect to $\omega$, the correctly renormalized sequence $(Z_n{)}_{n\ge 1}$ is proved to converge in distribution to a centered Gaussian law with explicit variance.

References in corpus (4)

• Scaling limit for trap models on ${\mathbb{Z}}^d$
• Exponential asymptotics and law of the iterated logarithm for intersection local times of random walks
• Random walk in random scenery: A survey of some recent results
• Convergence of dependent walks in a random scenery to fBm-local time fractional stable motions

Cited by in corpus (5)

• Persistence exponent for discrete-time, time-reversible processes
• Persistence probabilities for stationary increment processes
• CLT for random walks of commuting endomorphisms on compact abelian groups
• Survival asymptotics for branching random walks in IID environments
• Persistence exponent for random walk on directed versions of $Z^2$