Non-simple $\SLE$ curves are not determined by their range
View / Open Files
Authors
Miller, JP
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
Show full item recordCitation
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
Rights
Licence:
http://www.rioxx.net/licenses/all-rights-reserved
Statistics
Total file downloads (since January 2020). For more information on metrics see the
IRUS guide.
Recommended or similar items
The current recommendation prototype on the Apollo Repository will be turned off on 03 February 2023. Although the pilot has been fruitful for both parties, the service provider IKVA is focusing on horizon scanning products and so the recommender service can no longer be supported. We recognise the importance of recommender services in supporting research discovery and are evaluating offerings from other service providers. If you would like to offer feedback on this decision please contact us on: support@repository.cam.ac.uk