Reversibility conjecture for chordal SLE(κ;ρ+,ρ−)(\kappa;\rho_+,\rho_-) traces

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Let β0(t)\beta_0(t), 0≤t<∞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)\kappa\in(0,4) and ρ+,ρ−≥(κ−4)/2\rho_+,\rho_-\ge(\kappa-4)/2. Define

W0(z)=1z‾.W_0(z)=\frac{1}{\overline{z}}.

Reversibility conjecture. After a time-change, (W0(β0(1/t)))(W_0(\beta_0(1/t))), 0<t<∞0<t<\infty, has the same distribution as (β0(t))(\beta_0(t)), 0<t<∞0<t<\infty.

This conjecture concerns reversibility under inversion and time reversal for chordal SLE traces with force points on both sides of the starting point. The supplied context identifies it as a conjecture proposed in earlier work; no resolution is stated here.

References

Primary source

Dapeng Zhan, “Reversibility of Some Chordal SLE(κ;ρ) Traces”, arXiv:0807.3265 (2008).

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