Reversibility of whole-plane SLE for $κ> 8$
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909333314338816 |
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| author | Ang, Morris Yu, Pu |
| author_facet | Ang, Morris Yu, Pu |
| contents | Whole-plane SLE$_κ$ is a random fractal curve between two points on the Riemann sphere. Zhan established for $κ\leq 4$ that whole-plane SLE$_κ$ is reversible, meaning invariant in law under conformal automorphisms swapping its endpoints. Miller and Sheffield extended this to $κ\leq 8$. We prove whole-plane SLE$_κ$ is reversible for $κ> 8$, resolving the final case and answering a conjecture of Viklund and Wang. Our argument depends on a novel mating-of-trees theorem of independent interest, where Liouville quantum gravity on the disk is decorated by an independent radial space-filling SLE curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05176 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Reversibility of whole-plane SLE for $κ> 8$ Ang, Morris Yu, Pu Probability Mathematical Physics 60J67, 60G60 Whole-plane SLE$_κ$ is a random fractal curve between two points on the Riemann sphere. Zhan established for $κ\leq 4$ that whole-plane SLE$_κ$ is reversible, meaning invariant in law under conformal automorphisms swapping its endpoints. Miller and Sheffield extended this to $κ\leq 8$. We prove whole-plane SLE$_κ$ is reversible for $κ> 8$, resolving the final case and answering a conjecture of Viklund and Wang. Our argument depends on a novel mating-of-trees theorem of independent interest, where Liouville quantum gravity on the disk is decorated by an independent radial space-filling SLE curve. |
| title | Reversibility of whole-plane SLE for $κ> 8$ |
| topic | Probability Mathematical Physics 60J67, 60G60 |
| url | https://arxiv.org/abs/2309.05176 |