On the quenched functional CLT in random sceneries
Volume 269 / 2023
Studia Mathematica 269 (2023), 261-303
MSC: Primary 60F05; Secondary 28D05, 22D40, 60G50, 47B15, 37A25, 37A30.
DOI: 10.4064/sm210421-13-10
Published online: 12 December 2022
Abstract
We prove a quenched functional central limit theorem (quenched FCLT) for the sums of a random field (r.f.) along a $\mathbb Z^d$-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).
