Counter Examples to Invariant Circle Packing
Probability
2020-01-01 v1
Abstract
In this work, a unimodular random planar triangulation is constructed that has no invariant circle packing. This disputes a problem asked in [arXiv:1910.01614]. A natural weaker problem is the existence of point-stationary circle packings for a graph, which are circle packings that satisfy a certain mass transport principle. It is shown that the answer to this weaker problem is also false. Two examples are provided with two different approaches: Using indistinguishability and finite approximations.
Cite
@article{arxiv.1912.12862,
title = {Counter Examples to Invariant Circle Packing},
author = {Ali Khezeli},
journal= {arXiv preprint arXiv:1912.12862},
year = {2020}
}
Comments
21 pages, 5 figures