Welding of the Backward SLE and Tip of the Forward SLE

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• Zhan, D (Michigan State University)
• Thursday 18 June 2015, 15:20-16:20
• Seminar Room 1, Newton Institute.

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Random Geometry

Co-author: Steffen Rohde (University of Washington)

Let $kappain(0,4]$. A backward chordal SLE $_kappa$ process generates a conformal welding $phi$, which is a random auto-homeomorphism of $mathbb R$ that satisfies $phi^{-1}=phi$ and has a single fixed point: $0$. Using a stochastic coupling technique, we proved that the welding $phi$ satisfies the following symmetry: Let $h(z)=-1/z$. Then $h rc phi rc h$ has the same law as $phi$. Combining this symmetry result with the forward/backward SLE symmetry and the conformal removability of forward SLE curve, we then derived some ergodic property of the tip of a forward SLE $_kappa$ curve for $kappain(0,4)$.

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