Reversibility of chordal SLE with force points

From papers

Let β(t)\beta(t), 0t<0\le t<\infty, be a chordal SLE(κ;ρ,ρ+)(\kappa;\rho_-,\rho_+) trace started from (0;0,0+)(0;0^-,0^+), where

κ(0,4),ρ,ρ+κ/22.\kappa\in(0,4),\qquad \rho_-,\rho_+\ge \kappa/2-2.

Let W(z)=1/zW(z)=-1/z.

Reversibility of chordal SLE with force points. After a time-change, the reversal of (W(β(t)))(W(\beta(t))) has the same distribution as a chordal SLE(κ;ρ,ρ+)(\kappa;\rho_-,\rho_+) trace started from (0;0+,0)(0;0^+,0^-).

This asserts that inversion in the unit semicircle, followed by time reversal, preserves the law of the force-point SLE trace while interchanging the two force points. The supplied text does not state whether the result is proved or remains open.

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Sources & referencesView supporting material

Primary source

Dapeng Zhan, “Duality of Chordal SLE, II”, arXiv:0803.2223 (2008).

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