Random soups, carpets and fractal dimensions

被引：30

作者：

Nacu, Serban ^{[1
]}

Werner, Wendelin ^{[2
,3
]}

机构：

[1] Ecole Normale Super, Dept Math & Applicat, F-75230 Paris 05, France

[2] Univ Paris 11, Math Lab, F-91405 Orsay, France

[3] ENS, F-91405 Orsay, France

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2011年 / 83卷

关键词：

BROWNIAN LOOP; VALUES;

D O I：

10.1112/jlms/jdq094

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study some properties of a class of random connected planar fractal sets induced by a Poissonian scale-invariant and translation-invariant point process. Using the second-moment method, we show that their Hausdorff dimensions are deterministic and equal to their expectation dimension. We also estimate their low-intensity limiting behaviour. This applies in particular to the 'conformal loop ensembles' defined via Poissonian clouds of Brownian loops for which the expectation dimension has been computed by Schramm, Sheffield and Wilson.

引用

页码：789 / 809

页数：21

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