The Brownian loop soup

被引：149

作者：

Lawler, GF

Werner, W

机构：

[1] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

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

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2004年 / 128卷 / 04期

关键词：

Brownian loops; conformal invariance;

D O I：

10.1007/s00440-003-0319-6

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to "chronologically add Brownian loops" to simple curves in the plane.

引用

页码：565 / 588

页数：24

共 13 条

[1]

BELAVIN A, 1980, NUCL PHYS B, V241, P333

[2]

BILLINGSLEY P., 1999, Convergence of Probability Measures, V2nd, DOI 10.1002/9780470316962

[3] CONFORMAL-INVARIANCE AND SURFACE CRITICAL-BEHAVIOR [J].