Electronic Journal of Probability

From CLE($\kappa$) to SLE($\kappa,\rho$)'s

Wendelin Werner and Hao Wu

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 36, 20 pp.

Dates
Accepted: 12 March 2013
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064261

Digital Object Identifier
doi:10.1214/EJP.v18-2376

Mathematical Reviews number (MathSciNet)
MR3035764

Zentralblatt MATH identifier
1338.60205

Subjects
Primary: 60J67: Stochastic (Schramm-)Loewner evolution (SLE)
Secondary: 28A80: Fractals [See also 37Fxx]

Keywords
SLE CLE Conformal restriction Hausdorff dimension

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Werner, Wendelin; Wu, Hao. From CLE($\kappa$) to SLE($\kappa,\rho$)'s. Electron. J. Probab. 18 (2013), paper no. 36, 20 pp. doi:10.1214/EJP.v18-2376. https://projecteuclid.org/euclid.ejp/1465064261


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