The Intersection Probability of Brownian Motion and SLEκ

The Intersection Probability of Brownian Motion and SLEκ

By using excursion measure Poisson kernel method, we obtain a second-order differential equation of the intersection probability of Brownian motion and SLEκ. Moreover, we find a transformation such that the second-order differential equation transforms into a hypergeometric differential equation. Th...

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Main Authors: Shizhong Zhou, Shiyi Lan
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2015/627423
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spelling doaj-318c25317a0b408ab6d9f3d4064ba9962021-07-02T01:43:44ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/627423627423The Intersection Probability of Brownian Motion and SLEκShizhong Zhou0Shiyi Lan1Department of Statistics and Financial Mathematics, School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, ChinaSchool of Science, Guangxi University for Nationalities, Nanning, Guangxi 530006, ChinaBy using excursion measure Poisson kernel method, we obtain a second-order differential equation of the intersection probability of Brownian motion and SLEκ. 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 SLEκ and planar Brownian motion started from distinct points in an upper half-plane H-.http://dx.doi.org/10.1155/2015/627423
collection DOAJ
language English
format Article
sources DOAJ
author Shizhong Zhou
Shiyi Lan
spellingShingle Shizhong Zhou
Shiyi Lan
The Intersection Probability of Brownian Motion and SLEκ
Advances in Mathematical Physics
author_facet Shizhong Zhou
Shiyi Lan
author_sort Shizhong Zhou
title The Intersection Probability of Brownian Motion and SLEκ
title_short The Intersection Probability of Brownian Motion and SLEκ
title_full The Intersection Probability of Brownian Motion and SLEκ
title_fullStr The Intersection Probability of Brownian Motion and SLEκ
title_full_unstemmed The Intersection Probability of Brownian Motion and SLEκ
title_sort intersection probability of brownian motion and sleκ
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2015-01-01
description By using excursion measure Poisson kernel method, we obtain a second-order differential equation of the intersection probability of Brownian motion and SLEκ. 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 SLEκ and planar Brownian motion started from distinct points in an upper half-plane H-.
url http://dx.doi.org/10.1155/2015/627423
work_keys_str_mv AT shizhongzhou theintersectionprobabilityofbrownianmotionandslek
AT shiyilan theintersectionprobabilityofbrownianmotionandslek
AT shizhongzhou intersectionprobabilityofbrownianmotionandslek
AT shiyilan intersectionprobabilityofbrownianmotionandslek
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