Coin Tossing as a Billiard Problem
chao-dyn
2016-08-31 v2 Chaotic Dynamics
Abstract
We demonstrate that the free motion of any two-dimensional rigid body colliding elastically with two parallel, flat walls is equivalent to a billiard system. Using this equivalence, we analyze the integrable and chaotic properties of this new class of billiards. This provides a demonstration that coin tossing, the prototypical example of an independent random process, is a completely chaotic (Bernoulli) problem. The related question of which billiard geometries can be represented as rigid body systems is examined.
Cite
@article{arxiv.chao-dyn/9502011,
title = {Coin Tossing as a Billiard Problem},
author = {N. L. Balazs and Rupak Chatterjee and A. D. Jackson},
journal= {arXiv preprint arXiv:chao-dyn/9502011},
year = {2016}
}
Comments
16 pages, LaTex