We prove a quenched functional central limit theorem (quenched FCLT) for the sums of a random field (r.f.) along a Zd-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).
- exponential mixing
- flows on homogeneous spaces
- quenched functional central limit theorem
- random walk in random scenery
- self-intersections of a random walk
- toral automorphisms
All Science Journal Classification (ASJC) codes