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The Intersection Probability of Brownian Motion and SLE κ

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  • Shizhong Zhou
  • Shiyi Lan

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 .

Suggested Citation

  • Shizhong Zhou & Shiyi Lan, 2015. "The Intersection Probability of Brownian Motion and SLE κ," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-5, August.
    • Handle: RePEc:hin:jnlamp:627423
    DOI: 10.1155/2015/627423
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