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ファイル | 記述 | サイズ | フォーマット | |
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B59-21.pdf | 6.04 MB | Adobe PDF | 見る/開く |
タイトル: | Tutte polynomials and random-cluster models in Bernoulli cell complexes (Stochastic Analysis on Large Scale Interacting Systems) |
著者: | Hiraoka, Yasuaki Shirai, Tomoyuki |
著者名の別形: | ヒラオカ, ヤスアキ シライ, トモユキ |
キーワード: | 60C05 05C80 05E45 Bernoulli cell complex persistent homology Tutte polynomial random-cluster model |
発行日: | Jul-2016 |
出版者: | Research Institute for Mathematical Sciences, Kyoto University |
誌名: | 数理解析研究所講究録別冊 |
巻: | B59 |
開始ページ: | 289 |
終了ページ: | 304 |
抄録: | 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. |
記述: | "Stochastic Analysis on Large Scale Interacting Systems". October 26~29, 2015. edited by Ryoki Fukushima, Tadahisa Funaki, Yukio Nagahata, Makoto Nakashima, Hirofumi Osada and Yoshiki Otobe. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. |
著作権等: | © 2016 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved. |
URI: | http://hdl.handle.net/2433/243608 |
出現コレクション: | B59 Stochastic Analysis on Large Scale Interacting Systems |
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