On the quenched functional CLT in 2d random sceneries, examples
arXiv:1908.03777
summary
The paper proves a quenched functional central limit theorem for sums of a random field along a two‑dimensional random walk, covering iid random sceneries, fields generated by commuting torus automorphisms, and a Lorentz process version.
Abstract
We prove a quenched functional central limit theorem (quenched FCLT) for the sums of a random field (r.f.) along a 2d-random walk in different situations: when the r.f. is iid with a second order moment (random sceneries), or when it is generated by the action of commuting automorphisms of a torus. We consider also a quenched version of the FCLT when the random walk is replaced by a Lorentz process in the random scenery.
Topics & keywords
#random walk#random scenery#quenched functional CLT#torus automorphisms#Lorentz processquenched functional central limit theoremrandom field2d random walkiid random scenerycommuting automorphismstorusLorentz process