Reversibility of chordal SLE

106 citations recorded by the source corpus.

We prove that the chordal SLE κ trace is reversible for κ ∈ ( 0 , 4 ] .

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE$_{0+}$ (2016, background): “Proving this has turned out to be a challenge that resisted for some years, but has been settled by Zhan [30] in the case of the simple curves κ ∈ [0, 4], via rather non-trivial couplings of both ends of the path (see also Dubédat’s commutation relations [5], Miller and Sheffield’s approach based on”
Duality of chordal SLE (2007, methodology): “To prove this conjecture using the technique in [19] and this paper, one may need to know the conditional distribution of β(t), T1 ≤ t < T2, given its initial segment β([0, T1]) and final segment β([T2,∞)), where T1 is a stopping time, T2 is a “backward” stopping time, and T1 < T2.”
Imaginary geometry IV: interior rays, whole-plane reversibility, and space-filling trees (2013, background): “These reversibility results were shown for κ ≤ 8 in [14, 15, 16] (see also [32, 34, 2]) and will be established for κ > 8 here.”
Conformal loop ensembles: the Markovian characterization and the loop-soup construction (2010, background): “It has been proved by Dapeng Zhan that SLEκ for κ ≤ 4 is indeed reversible (see [46]), which in fact implies this last statement.”
SLE and the free field: partition functions and couplings (2007, background): “In the context of SLE reversibility, Zhan showed in [42] how to lift local couplings to global couplings.”