Tutte polynomials and random-cluster models in Bernoulli cell complexes
Probability
2016-02-16 v1 Algebraic Topology
Combinatorics
Abstract
This paper studies Bernoulli cell complexes from the perspective of persistent homology, Tutte polynomials, and random-cluster models. Following the previous work [9], we first show the asymptotic order of the expected lifetime sum of the persistent homology for the Bernoulli cell complex process on the -cubical lattice. Then, an explicit formula of the expected lifetime sum using the Tutte polynomial is derived. Furthermore, we study a higher dimensional generalization of the random-cluster model derived from the Edwards-Sokal type coupling, and show some basic results such as the positive association and the relation to the Tutte polynomial.
Cite
@article{arxiv.1602.04561,
title = {Tutte polynomials and random-cluster models in Bernoulli cell complexes},
author = {Yasuaki Hiraoka and Tomoyuki Shirai},
journal= {arXiv preprint arXiv:1602.04561},
year = {2016}
}