  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.
