This was part of Random Explorations

Loewner energy reversibility via local reversals

Jinwoo Sung, University of Washington

Tuesday, July 7, 2026



Slides
Abstract: The Loewner energy of a chord in a simply connected planar domain is defined as the Dirichlet energy of the driving function for the corresponding Loewner chain. A fundamental property is its reversibility, which means that the energy of a chord does not depend on the direction in which it is unzipped by a Loewner chain. Yilin Wang first proved this property using the reversibility of chordal Schramm–Loewner evolution (SLE), identifying Loewner energy as the large deviation rate function for chordal SLE as κ decreases to 0. I will present a deterministic proof of this fact by reversing the chord in small increments, using the commutation relations of Loewner energy. Along the way, I will highlight similarities with and differences from the proofs of SLE reversibility by Dapeng Zhan and by Greg Lawler and Stephen Yearwood.