The Intersection Probability of Brownian Motion and SLEk

被引：0
|
作者：
Zhou, Shizhong [1 ,2 ]
Lan, Shiyi [2 ]
机构：
[1] Nanjing Univ Sci & Technol, Dept Stat & Financial Math, Nanjing 210094, Jiangsu, Peoples R China
[2] Guangxi Univ Nationalities, Sch Sci, Nanning 530006, Guangxi, Peoples R China
来源：
ADVANCES IN MATHEMATICAL PHYSICS | 2015年 / 2015卷
基金：
中国国家自然科学基金;
关键词：
PLANE EXPONENTS; VALUES;
D O I：
10.1155/2015/627423
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
By using excursion measure Poisson kernel method, we obtain a second-order differential equation of the intersection probability of Brownian motion and SLEk. Moreover, we find a transformation such that the second-order differential equation transforms into a hypergeometric differential equation. Then, by solving the hypergeometric differential equation, we obtain the explicit formula of the intersection probability for the trace of the chordal SLEk. and planar Brownian motion started from distinct points in an upper half-plane (H) over bar.
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页数：5
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