Random walks in Euclidean space
Dynamical Systems
2015-08-17 v3 Group Theory
Probability
Abstract
Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove a local limit theorem under a suitable moment condition and a necessary non-degeneracy condition. Under stronger hypothesis, we prove a limit theorem on a wide range of scales: between e^(-cl^(1/4)) and l^(1/2), where l is the number of steps.
Cite
@article{arxiv.1205.3399,
title = {Random walks in Euclidean space},
author = {Péter Pál Varjú},
journal= {arXiv preprint arXiv:1205.3399},
year = {2015}
}
Comments
62 pages, 1 figure, revision based on referee's report, proofs and results unchanged