Exploration trees and conformal loop ensembles
Probability
2007-05-23 v2 Mathematical Physics
Complex Variables
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.math/0609167,
title = {Exploration trees and conformal loop ensembles},
author = {Scott Sheffield},
journal= {arXiv preprint arXiv:math/0609167},
year = {2007}
}
Comments
57 pages, 5 figures