Non-simple $\SLE$ curves are not determined by their range
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Authors
Miller, Jason
Sheffield, Scott
Werner, Wendelin
Publication Date
2020Journal Title
Journal of the European Mathematical Society
ISSN
1435-9863
Publisher
European Mathematical Society Publishing House
Volume
22
Issue
3
Pages
669-716
Type
Article
This Version
AM
Metadata
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Miller, J., Sheffield, S., & Werner, W. (2020). Non-simple $\SLE$ curves are not determined by their range. Journal of the European Mathematical Society, 22 (3), 669-716. https://doi.org/10.4171/JEMS/930
Abstract
We show that when observing the range of a chordal $\SLE_\kappa$ curve for $\kappa \in (4,8)$, it is not possible to recover the order in which the points have been visited. We also derive related results about conformal loop ensembles (CLE):
(i) The loops in a $\CLE_\kappa$ for $\kappa \in (4,8)$ are not determined by the $\CLE_\kappa$ gasket.
(ii) The continuum percolation interfaces defined in the fractal carpets of conformal loop ensembles $\CLE_{\kappa}$ for $\kappa \in (8/3, 4)$ (we defined these percolation interfaces
in earlier work, where we also showed there that they are $\SLE_{16/\kappa}$ curves) are not determined by the $\CLE_{\kappa}$ carpet that they are defined in.
Identifiers
External DOI: https://doi.org/10.4171/JEMS/930
This record's URL: https://www.repository.cam.ac.uk/handle/1810/288185
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