Random Kleinian Groups I: Random Fuchsian Groups
Complex Variables
2017-12-12 v1
Abstract
We introduce a geometrically natural probability measure on the group of all M\"obius transformations of the circle. Our aim is to study "random" groups of M\"obius transformations, and in particular random two-generator groups. By this we mean groups where the generators are selected randomly. The probability measure in effect establishes an isomorphism between random -generators groups and collections of random pairs of arcs on the circle. Our aim is to estimate the likely-hood that such a random group is discrete, calculate the expectation of their associated parameters, geometry and topology, and to test the effectiveness of tests for discreteness such as J{\o}rgensen's inequality.
Cite
@article{arxiv.1712.03602,
title = {Random Kleinian Groups I: Random Fuchsian Groups},
author = {Gaven Martin and Graeme O'Brien},
journal= {arXiv preprint arXiv:1712.03602},
year = {2017}
}