A note on Loewner energy, conformal restriction and Werner's measure on self-avoiding loops
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arXiv
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866909091413098496 |
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| author | Wang, Yilin |
| author_facet | Wang, Yilin |
| contents | In this note, we establish an expression of the Loewner energy of a Jordan curve on the Riemann sphere in terms of Werner's measure on simple loops of SLE$_{8/3}$ type. The proof is based on a formula for the change of the Loewner energy under a conformal map that is reminiscent of the restriction properties derived for SLE processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_04578 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A note on Loewner energy, conformal restriction and Werner's measure on self-avoiding loops Wang, Yilin Complex Variables Probability In this note, we establish an expression of the Loewner energy of a Jordan curve on the Riemann sphere in terms of Werner's measure on simple loops of SLE$_{8/3}$ type. The proof is based on a formula for the change of the Loewner energy under a conformal map that is reminiscent of the restriction properties derived for SLE processes. |
| title | A note on Loewner energy, conformal restriction and Werner's measure on self-avoiding loops |
| topic | Complex Variables Probability |
| url | https://arxiv.org/abs/1810.04578 |