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このアイテムのファイル:
| ファイル | 記述 | サイズ | フォーマット | |
|---|---|---|---|---|
| B79-13.pdf | 123.2 kB | Adobe PDF | 見る/開く |
| タイトル: | On persistent homology of random Cech complexes (Stochastic Analysis on Large Scale Interacting Systems) |
| 著者: | Trinh, Khanh Duy |
| キーワード: | 60K35 55N20 Cech complex critical simplex generalized discrete Morse theory persistence diagram binomial point process |
| 発行日: | Apr-2020 |
| 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: | B79 |
| 開始ページ: | 215 |
| 終了ページ: | 228 |
| 抄録: | The paper studies the relation between critical simplices and persistence diagrams of the Cech filtration. We show that adding a critical k-simplex into the filtration corresponds either to a point in the kth persistence diagram or a point in the (k - 1)st persistence diagram. Consequently, the number of points in persistence diagrams can be expressed in terms of the number of critical simplices. As an application, we establish some convergence results related to persistence diagrams of the Cech filtrations built over binomial point processes. |
| 記述: | "Stochastic Analysis on Large Scale Interacting Systems". November 5-8, 2018. edited by Ryoki Fukushima, Tadahisa Funaki, Yukio Nagahata, Hirofumi Osada and Kenkichi Tsunoda. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. |
| 著作権等: | © 2020 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved. |
| URI: | http://hdl.handle.net/2433/260653 |
| 出現コレクション: | B79 Stochastic Analysis on Large Scale Interacting Systems |
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