Reversibility conjecture for whole-plane SLE

From papers

Let κ(0,4]\kappa\in(0,4], and let β\beta be a whole-plane SLEκ_\kappa trace in the Riemann sphere C^\widehat{\mathbb C}, growing from a point \a\a to a point \b\b. Reversibility means that, after a time-change, the reversal of β\beta has the same distribution as a whole-plane SLEκ_\kappa trace from \b\b to \a\a.

Whole-plane SLE reversibility conjecture. The whole-plane SLEκ_\kappa trace satisfies reversibility for κ(0,4]\kappa\in(0,4].

The conjecture is the whole-plane analogue of chordal SLE reversibility, and is relevant to identifying reversals of radial SLE traces. The supplied text presents it as the goal of the paper and gives no evidence of resolution, so its status is left open here.

Progress summary

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Sources & referencesView supporting material

Primary source

Dapeng Zhan, “On the reversal of radial SLE, I: Commutation Relations in Annuli”, arXiv:0904.0808 (2017).

Additional references

2 papers in this index state this conjecture (2006–2009). The statement above is taken from the most recent of them; the others are arXiv:math/0609167.

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