From CLE(\kappa) to SLE(\kappa,\rho)'s
Wendelin Werner, Hao Wu
TL;DR
This paper presents a method to connect loops in a Conformal Loop Ensemble to generate samples of SLE() and SLE(,) processes, revealing new insights into their relationships.
Contribution
It introduces a novel construction linking CLE loops to SLE() and SLE(,) processes, enhancing understanding of their interplay.
Findings
Constructs SLE() and SLE(,) from CLE loops
Provides insights into the relationship between CLE and SLE processes
Discusses implications of the construction for conformal invariance
Abstract
We show how to connect together the loops of a simple Conformal Loop Ensemble (CLE) in order to construct samples of chordal SLE(\kappa) processes and their SLE(\kappa,\rho) variants, and we discuss some consequences of this construction.
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Taxonomy
TopicsChaos control and synchronization · Mathematical Dynamics and Fractals · Cellular Automata and Applications