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jmsj_79777977.pdf | 8.72 MB | Adobe PDF | 見る/開く |
タイトル: | Asymptotic behavior of lifetime sums for random simplicial complex processes |
著者: | HINO, Masanori ![]() ![]() ![]() KANAZAWA, Shu |
著者名の別形: | 日野, 正訓 金澤, 秀 |
キーワード: | Linial–Meshulam complex process random clique complex process multi-parameter random simplicial complex lifetime sum Betti number |
発行日: | Jul-2019 |
出版者: | Mathematical Society of Japan |
誌名: | Journal of the Mathematical Society of Japan |
巻: | 71 |
号: | 3 |
開始ページ: | 765 |
終了ページ: | 804 |
抄録: | We study the homological properties of random simplicial complexes. In particular, we obtain the asymptotic behavior of lifetime sums for a class of increasing random simplicial complexes; this result is a higher-dimensional counterpart of Frieze's ζ(3)-limit theorem for the Erdős–Rényi graph process. The main results include solutions to questions posed in an earlier study by Hiraoka and Shirai about the Linial–Meshulam complex process and the random clique complex process. One of the key elements of the arguments is a new upper bound on the Betti numbers of general simplicial complexes in terms of the number of small eigenvalues of Laplacians on links. This bound can be regarded as a quantitative version of the cohomology vanishing theorem. |
著作権等: | © 2019 Mathematical Society of Japan The full-text file will be made open to the public on 1 July 2022 in accordance with publisher's 'Terms and Conditions for Self-Archiving'. |
URI: | http://hdl.handle.net/2433/243268 |
DOI(出版社版): | 10.2969/jmsj/79777977 |
関連リンク: | https://projecteuclid.org/euclid.jmsj/1556092819 |
出現コレクション: | 学術雑誌掲載論文等 |
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