Duke Mathematical Journal

Exploration trees and conformal loop ensembles

Scott Sheffield

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We construct and study the conformal loop ensembles CLE(κ), defined for 8/3κ8, using branching variants of SLE(κ) called exploration trees. The CLE(κ) are random collections of countably many loops in a planar domain that are characterized by certain conformal invariance and Markov properties. We conjecture that they are the scaling limits of various random loop models from statistical physics, including the O(n) loop models

Article information

Duke Math. J., Volume 147, Number 1 (2009), 79-129.

First available in Project Euclid: 26 February 2009

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Zentralblatt MATH identifier

Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 82B27: Critical phenomena


Sheffield, Scott. Exploration trees and conformal loop ensembles. Duke Math. J. 147 (2009), no. 1, 79--129. doi:10.1215/00127094-2009-007. https://projecteuclid.org/euclid.dmj/1235657189

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