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Critical intensities of Boolean models with different underlying convex shapes 

作成者 Roy, Rahul, 種村, 秀紀
作成者の別表記 Tanemura, Hideki
キーワード等 Poisson process, Boolean model, percolation, critical intensity
日本十進分類法 (NDC) 410
内容 We consider the Poisson Boolean model of percolation where the percolating shapes are convex regions. By an enhancement argument we strengthen a result of Jonasson (2000) to show that the critical intensity of percolation in two dimensions is minimized among the class of convex shapes of unit area when the percolating shapes are triangles, and, for any other shape, the critical intensity is strictly larger than this minimum value. We also obtain a partial generalization to higher dimensions. In particular, for three dimensions, the critical intensity of percolation is minimized among the class of regular polytopes of unit volume when the percolating shapes are tetrahedrons. Moreover, for any other regular polytope, the critical intensity is strictly larger than this minimum value.
コンテンツの種類 雑誌掲載論文 Journal Article
ファイル形式 application/x-dvi
ハンドルURL http://mitizane.ll.chiba-u.jp/meta-bin/mt-pdetail.cgi?cd=00020932
DOI 10.1239/aap/1019160949
掲載誌情報 Advances in applied probability Vol.34 no.1 page.48-57 (2002)
フルテキストへのリンク http://mitizane.ll.chiba-u.jp/metadb/up/C0000050988/MR1895330.dvi
言語 英語
関連情報 (hasVersion) http://dx.doi.org/10.1239/aap/1019160949
著者版フラグ author


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Poisson process
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