Tutte多项式与Bernoulli胞腔复形中的随机簇模型
Tutte polynomials and random-cluster models in Bernoulli cell complexes
摘要：
本文从持续同调、Tutte多项式和随机簇模型的角度研究了Bernoulli胞腔复形。在文献[9]的基础上，我们首先给出了$\ell$ -立方格上Bernoulli胞腔复形过程的持久同调的期望寿命和的渐近阶.然后，使用Tutte多项式的期望寿命和的显式公式推导。此外，我们研究了由Edwards-Sokal型耦合导出的随机簇模型的高维推广，并给出了一些基本结果，如正关联和与Tutte多项式的关系。
英文摘要：
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.
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