From the random geometry of conformally invariant systems to the Kähler geometry of universal Teichmüller space
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911772917628928 |
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| author | Wang, Yilin |
| author_facet | Wang, Yilin |
| contents | The goal of this expository article is to explain how a fundamental functional on the space of Jordan curves arising from SLE - Loewner energy - is connected to a seemingly far apart subject: the Kähler geometry of universal Teichmüller space. We provide a background on Loewner energy, the universal Liouville action, and the intuition behind the proof of the identity between them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05301 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | From the random geometry of conformally invariant systems to the Kähler geometry of universal Teichmüller space Wang, Yilin Probability Complex Variables The goal of this expository article is to explain how a fundamental functional on the space of Jordan curves arising from SLE - Loewner energy - is connected to a seemingly far apart subject: the Kähler geometry of universal Teichmüller space. We provide a background on Loewner energy, the universal Liouville action, and the intuition behind the proof of the identity between them. |
| title | From the random geometry of conformally invariant systems to the Kähler geometry of universal Teichmüller space |
| topic | Probability Complex Variables |
| url | https://arxiv.org/abs/2308.05301 |