Tutte polynomials and random-cluster models in Bernoulli cell complexes

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 $\ell$-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.

Cited by in corpus (2)

• Randomly Weighted $d-$complexes: Minimal Spanning Acycles and Persistence Diagrams
• Limit theorems for random cubical homology