Non-simple SLE curves are not determined by their range
© European Mathematical Society 2020 We show that when observing the range of a chordal SLEκ curve for κ ∈ (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 CLEκ for κ ∈ (4, 8...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
European Mathematical Society Publishing House
2021
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| Online Access: | https://hdl.handle.net/1721.1/135914 |
| _version_ | 1826191446522200064 |
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| author | Miller, Jason Sheffield, Scott Werner, Wendelin |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Miller, Jason Sheffield, Scott Werner, Wendelin |
| author_sort | Miller, Jason |
| collection | MIT |
| description | © European Mathematical Society 2020 We show that when observing the range of a chordal SLEκ curve for κ ∈ (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 CLEκ for κ ∈ (4, 8) are not determined by the CLEκ gasket. (ii) The continuum percolation interfaces defined in the fractal carpets of conformal loop ensembles CLEκ for κ ∈ (8/3, 4) (we defined these percolation interfaces in earlier work, where we also showed that they are SLE16/κ curves) are not determined by the CLEκ carpet that they are defined in. |
| first_indexed | 2024-09-23T08:55:59Z |
| format | Article |
| id | mit-1721.1/135914 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:55:59Z |
| publishDate | 2021 |
| publisher | European Mathematical Society Publishing House |
| record_format | dspace |
| spelling | mit-1721.1/1359142023-12-08T20:36:57Z Non-simple SLE curves are not determined by their range Miller, Jason Sheffield, Scott Werner, Wendelin Massachusetts Institute of Technology. Department of Mathematics © European Mathematical Society 2020 We show that when observing the range of a chordal SLEκ curve for κ ∈ (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 CLEκ for κ ∈ (4, 8) are not determined by the CLEκ gasket. (ii) The continuum percolation interfaces defined in the fractal carpets of conformal loop ensembles CLEκ for κ ∈ (8/3, 4) (we defined these percolation interfaces in earlier work, where we also showed that they are SLE16/κ curves) are not determined by the CLEκ carpet that they are defined in. 2021-10-27T20:29:56Z 2021-10-27T20:29:56Z 2019 2021-05-26T16:13:38Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/135914 en 10.4171/JEMS/930 Journal of the European Mathematical Society Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf European Mathematical Society Publishing House arXiv |
| spellingShingle | Miller, Jason Sheffield, Scott Werner, Wendelin Non-simple SLE curves are not determined by their range |
| title | Non-simple SLE curves are not determined by their range |
| title_full | Non-simple SLE curves are not determined by their range |
| title_fullStr | Non-simple SLE curves are not determined by their range |
| title_full_unstemmed | Non-simple SLE curves are not determined by their range |
| title_short | Non-simple SLE curves are not determined by their range |
| title_sort | non simple sle curves are not determined by their range |
| url | https://hdl.handle.net/1721.1/135914 |
| work_keys_str_mv | AT millerjason nonsimpleslecurvesarenotdeterminedbytheirrange AT sheffieldscott nonsimpleslecurvesarenotdeterminedbytheirrange AT wernerwendelin nonsimpleslecurvesarenotdeterminedbytheirrange |