On the quenched functional CLT in random sceneries
arXiv:2104.12397
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).
arXiv admin note: substantial text overlap with arXiv:1908.03777