On the quenched functional CLT in random sceneries

TL;DR

This paper establishes a quenched functional central limit theorem for sums of random fields along random walks, covering probabilistic and algebraic frameworks, advancing understanding of asymptotic behaviors in complex stochastic systems.

Contribution

It proves a quenched FCLT for random fields along random walks in both probabilistic and algebraic settings, extending previous results to new classes of systems.

Findings

Quenched FCLT holds for i.i.d. and moving average random fields.

Results apply to systems generated by automorphisms of a torus.

Applicable to hyperbolic flows on homogeneous spaces.

Abstract

We prove a quenched functional central limit theorem (quenched FCLT) for the sums of a random field (r.f.) along a Z d-random walk in different frameworks: probabilistic (when the r.f. is i.i.d. or a moving average of i.i.d. random variables) and algebraic (when the r.f. is generated by commuting automorphisms of a torus or by commuting hyperbolic flows on homogeneous spaces).