Tutte polynomials and random-cluster models in Bernoulli cell complexes (Stochastic Analysis on Large Scale Interacting Systems)

ヒラオカ, ヤスアキ, シライ, トモユキ

説明

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 ℓ-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.

収録刊行物

数理解析研究所講究録別冊

数理解析研究所講究録別冊 B59 289-304, 2016-07

Research Institute for Mathematical Sciences, Kyoto University

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詳細情報詳細情報について

CRID: 1050564288413953920

NII論文ID: 120006715340

NII書誌ID: AA12196120

ISSN: 18816193

HANDLE: 2433/243608

本文言語コード: en

資料種別: departmental bulletin paper

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