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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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/627423 |
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| _version_ | 1850106066316034048 |
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| author | Shizhong Zhou Shiyi Lan |
| author_facet | Shizhong Zhou Shiyi Lan |
| author_sort | Shizhong Zhou |
| collection | DOAJ |
| 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-. |
| format | Article |
| id | doaj-art-318c25317a0b408ab6d9f3d4064ba996 |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-318c25317a0b408ab6d9f3d4064ba9962025-08-20T02:38:54ZengWileyAdvances 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 |
| spellingShingle | Shizhong Zhou Shiyi Lan The Intersection Probability of Brownian Motion and SLEκ Advances in Mathematical Physics |
| title | 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_short | The Intersection Probability of Brownian Motion and SLEκ |
| title_sort | intersection probability of brownian motion and sleκ |
| url | http://dx.doi.org/10.1155/2015/627423 |
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