Exploration trees and conformal loop ensembles

Details Exploration trees and conformal loop ensembles Exploration trees and conformal loop ensembles

2006-09-06

arxiv.org/abs/math/0609167v2

Mathematics

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57 pages, 5 figures

Scientific paper

We construct and study the conformal loop ensembles CLE(kappa), defined for all kappa between 8/3 and 8, using branching variants of SLE(kappa) called exploration trees. The conformal loop ensembles 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.

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