論文

査読有り
2019年2月

Strong Law of Large Numbers for Betti Numbers in the Thermodynamic Regime

JOURNAL OF STATISTICAL PHYSICS
  • Akshay Goel
  • ,
  • Khanh Duy Trinh
  • ,
  • Kenkichi Tsunoda

174
4
開始ページ
865
終了ページ
892
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1007/s10955-018-2201-z
出版者・発行元
SPRINGER

We establish the strong law of large numbers for Betti numbers of random ech complexes built on RN-valued binomial point processes and related Poisson point processes in the thermodynamic regime. Here we consider both the case where the underlying distribution of the point processes is absolutely continuous with respect to the Lebesgue measure on RN and the case where it is supported on a C1 compact manifold of dimension strictly less than N. The strong law is proved under very mild assumption which only requires that the common probability density function belongs to Lp spaces, for all 1p<.

Web of Science ® 被引用回数 : 3

リンク情報
DOI
https://doi.org/10.1007/s10955-018-2201-z
arXiv
http://arxiv.org/abs/arXiv:1805.05032
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000458794600007&DestApp=WOS_CPL
Arxiv Url
http://arxiv.org/abs/1805.05032v2
Arxiv Url
http://arxiv.org/pdf/1805.05032v2 本文へのリンクあり

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