The Intersection Probability of Brownian Motion and SLE κ

Shizhong Zhou and Shiyi Lan

Advances in Mathematical Physics, 2015, vol. 2015, 1-5

Abstract:

By using excursion measure Poisson kernel method, we obtain a second-order differential equation of the intersection probability of Brownian motion and . 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 and planar Brownian motion started from distinct points in an upper half-plane .

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:627423

DOI: 10.1155/2015/627423

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