Onsager-Machlup functional for $\text{SLE}_κ$ loop measures
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909197235388416 |
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| author | Carfagnini, Marco Wang, Yilin |
| author_facet | Carfagnini, Marco Wang, Yilin |
| contents | We relate two ways to renormalize the Brownian loop measure on the Riemann sphere. One by considering the Brownian loop measure on the sphere minus a small disk, known as the normalized Brownian loop measure; the other by taking the measure on simple loops induced by the outer boundary of the Brownian loops, known as Werner's measure. This result allows us to interpret the Loewner energy as an Onsager--Machlup functional for SLE$_κ$ loop measure for any fixed $κ\in (0, 4]$, and more generally, for any Malliavin--Kontsevich--Suhov loop measure of the same central charge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00209 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Onsager-Machlup functional for $\text{SLE}_κ$ loop measures Carfagnini, Marco Wang, Yilin Probability Mathematical Physics Complex Variables We relate two ways to renormalize the Brownian loop measure on the Riemann sphere. One by considering the Brownian loop measure on the sphere minus a small disk, known as the normalized Brownian loop measure; the other by taking the measure on simple loops induced by the outer boundary of the Brownian loops, known as Werner's measure. This result allows us to interpret the Loewner energy as an Onsager--Machlup functional for SLE$_κ$ loop measure for any fixed $κ\in (0, 4]$, and more generally, for any Malliavin--Kontsevich--Suhov loop measure of the same central charge. |
| title | Onsager-Machlup functional for $\text{SLE}_κ$ loop measures |
| topic | Probability Mathematical Physics Complex Variables |
| url | https://arxiv.org/abs/2311.00209 |