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Commutation relations for Schramm‐Loewner evolutions
Author(s) -
Dubédat Julien
Publication year - 2007
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20191
Subject(s) - infinitesimal , mathematics , commutation , lift (data mining) , simple (philosophy) , domain (mathematical analysis) , conformal map , pure mathematics , plane (geometry) , mathematical analysis , geometry , computer science , physics , quantum mechanics , philosophy , epistemology , voltage , data mining
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.