Commutation relations for Schramm‐Loewner evolutions

By Julien Dubédat. 2004

133 citations recorded by the source corpus.

Schramm‐Loewner evolutions (SLEs) describe a one‐parameter family of growth processes in the plane that have particular conformal invariance properties. For instance, SLE can define simple random curves in a simply connected domain. In this paper we are interested in questions pertaining to the definition of several SLEs in a domain (i.e., several random curves). In particular, we derive infinitesimal commutation conditions, discuss some elementary solutions, study integrability conditions following from commutation, and show how to lift these infinitesimal relations to global relations in simple cases. The situation in multiply connected domains is also discussed. © 2007 Wiley Periodicals, Inc.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/11cdc41561bfd0a8485326306d477594e7ee722c

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In Applied Mathematics

1. Yilin Wang
2. Dapeng Zhan

Citations in the corpus

• The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE$_{0+}$ (2016, background): “I am also grateful to Steffen Rohde for his comments on the first draft, to Julien Dubédat for nicely pointing out the similar idea in [5], to Yves Le Jan for conversations on the topic and to the referees for very helpful comments on the first version of this paper.”
• Reversibility of chordal SLE (2008, background): “Some computations were done in [3, 4, 5] and other papers.”