Abstract
The family of exploration processes with parameter forms a natural class of conformally invariant ways for discovering the loops of a conformal loop ensemble . Such an exploration consists of one simple continuous path called the trunk of the exploration that discovers loops along the way. The parameter μ appears in the Loewner chain description of the path that traces the trunk and all loops encountered by the trunk in chronological order. These explorations can also be interpreted in terms of level lines of a Gaussian free field.
It has been shown by Miller, Sheffield and Werner that the trunk of such an exploration is an process for some (unknown) value of . The main result of the present paper is to establish the relation between μ and ρ, more specifically to show that .
Funding Statement
The author was supported by grant 175505 of the Swiss National Science Foundation and is part of SwissMAP.
Acknowledgments
The author would like to thank Wendelin Werner for many insightful inputs throughout this project and the anonymous referee for helpful comments.
Citation
Matthis Lehmkuehler. "The trunks of CLE(4) explorations." Ann. Appl. Probab. 33 (5) 3387 - 3417, October 2023. https://doi.org/10.1214/22-AAP1895
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