Exploration trees and conformal loop ensembles

@inproceedings{Sheffield2006ExplorationTA,
  title={Exploration trees and conformal loop ensembles},
  author={Scott Sheffield},
  year={2006}
}
We construct and study the conformal loop ensembles CLE(κ), defined for 8/3 ≤ κ ≤ 8, 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. ∗Courant Institute, NYU. Partially supported by NSF grant DMS… CONTINUE READING

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