Limiting distribution of visits of sereval rotations to shrinking intervals
Dynamical Systems
2010-05-11 v1 Number Theory
Abstract
We show that given normalized intervals on the unit circle, the numbers of visits of random rotations to these intervals have a joint limiting distribution as lengths of trajectories tend to infinity. If then tends to infinity, then the numbers of points in different intervals become asymptotically independent unless an arithmetic obstruction arises. This is a generalization of earlier results of J. Marklof.
Keywords
Cite
@article{arxiv.1005.1622,
title = {Limiting distribution of visits of sereval rotations to shrinking intervals},
author = {Ilya Vinogradov},
journal= {arXiv preprint arXiv:1005.1622},
year = {2010}
}