A deterministic proof of Loewner energy reversibility via local reversals
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913535325372416 |
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| author | Sung, Jinwoo |
| author_facet | Sung, Jinwoo |
| contents | We give a new proof of the orientation reversibility of chordal Loewner energy by reversing the orientation of a chord in partial increments. This fact was first proved by Yilin Wang (arXiv:1601.05297) using the reversibility of chordal Schramm-Loewner evolution (SLE) along with the interpretation of Loewner energy as the large deviation rate function of chordal SLE$_κ$ as $κ\to 0$. Our method is similar in spirit to Dapeng Zhan's proof (arXiv:0808.3649) of chordal SLE$_κ$ reversibility for $κ\in (0,4]$, though it is purely deterministic. As a key step in our proof, we establish that a minimimal energy chord among those passing through a fixed finite set of points is a piecewise hyperbolic geodesic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21769 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A deterministic proof of Loewner energy reversibility via local reversals Sung, Jinwoo Complex Variables Probability We give a new proof of the orientation reversibility of chordal Loewner energy by reversing the orientation of a chord in partial increments. This fact was first proved by Yilin Wang (arXiv:1601.05297) using the reversibility of chordal Schramm-Loewner evolution (SLE) along with the interpretation of Loewner energy as the large deviation rate function of chordal SLE$_κ$ as $κ\to 0$. Our method is similar in spirit to Dapeng Zhan's proof (arXiv:0808.3649) of chordal SLE$_κ$ reversibility for $κ\in (0,4]$, though it is purely deterministic. As a key step in our proof, we establish that a minimimal energy chord among those passing through a fixed finite set of points is a piecewise hyperbolic geodesic. |
| title | A deterministic proof of Loewner energy reversibility via local reversals |
| topic | Complex Variables Probability |
| url | https://arxiv.org/abs/2407.21769 |