On the Rate of Convergence of Loop-Erased Random Walk to SLE2

被引：11

作者：

Benes, Christian ^{[1
]}

Viklund, Fredrik Johansson ^{[2
]}

Kozdron, Michael J. ^{[3
]}

机构：

[1] CUNY Brooklyn Coll, Dept Math, Brooklyn, NY 11210 USA

[2] Columbia Univ, Dept Math, New York, NY 10027 USA

[3] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2013年 / 318卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

BROWNIAN INTERSECTION EXPONENTS; CONFORMAL-INVARIANCE; VALUES; PLANE;

D O I：

10.1007/s00220-013-1666-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We derive a rate of convergence of the Loewner driving function for a planar loop-erased random walk to Brownian motion with speed 2 on the unit circle, the Loewner driving function for radial SLE2. The proof uses a new estimate of the difference between the discrete and continuous Green's functions that is an improvement over existing results for the class of domains we consider. Using the rate for the driving process convergence along with additional information about SLE2, we also obtain a rate of convergence for the paths with respect to the Hausdorff distance.

引用

页码：307 / 354

页数：48

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