Limiting distribution of visits of sereval rotations to shrinking intervals

Details Limiting distribution of visits of sereval rotations to shrinking intervals Limiting distribution of visits of sereval rotations to shrinking intervals

2010-05-10

arxiv.org/abs/1005.1622v1

Mathematics

Dynamical Systems

Scientific paper

We show that given $n$ normalized intervals on the unit circle, the numbers of visits of $d$ random rotations to these intervals have a joint limiting distribution as lengths of trajectories tend to infinity. If $d$ 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.

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