Backward SLE and the symmetry of the welding

2013/07/09 by Steffen Rohde, Rohde, Steffen, Dapeng Zhan +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1307.2532

openalex publication_date 2013/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The backward chordal Schramm-Loewner Evolution naturally defines a conformal welding homeomorphism of the real line. We show that this homeomorphism is invariant under the automorphism x↦ -1/x, and conclude that the associated solution to the welding problem (which is a natural renormalized limit of the finite time Loewner traces) is reversible. The proofs rely on an analysis of the action of analytic circle diffeomorphisms on the space of hulls, and on the coupling techniques of the second author.

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