2004/11/30 by Julien Dubédat, Julien Dubedat · 3 citations
Mathematics · #Commutation #Conformal map #Domain (mathematical analysis) #Geometric Analysis and Curvature Flows #Infinitesimal #Lift (data mining) #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #Simple (philosophy) #math.PR #msc:60G17 #msc:60G52 #msc:60K35
paper · pdf · doi:10.1002/cpa.20191
published as Comm. Pure Applied Mathematics. 60 (12), p 1792--1847, 2007 · v3: several corrections and additional material. 42 pages
arxiv created 2005/12/06 · openalex publication_date 2007/05/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Abstract 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.