Multi-time Loewner energy: rate function for large deviation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911464583856128 |
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| author | Chen, Mo Huang, Chongzhi Wu, Hao |
| author_facet | Chen, Mo Huang, Chongzhi Wu, Hao |
| contents | The classification of probability measures that satisfy both conformal invariance and domain Markov property is equivalent to characterizing solutions to the Belavin--Polyakov--Zamolodchikov (BPZ) equations, as established by Dubédat~[Dub07]. In this context, the partition functions for half-watermelon SLE and for multi-radial SLE serve as fundamental solutions to the BPZ equations. In this article, we investigate the large deviation principle for both half-watermelon SLE and multi-radial SLE. The associated rate function is given by the multi-time Loewner energy, introduced in~[CHPW26]. As applications, we provide an alternative proof of the large deviation principle for Dyson Brownian motion, as well as a new derivation of the boundary perturbation property of the multi-time Loewner energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20642 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multi-time Loewner energy: rate function for large deviation Chen, Mo Huang, Chongzhi Wu, Hao Probability 60J67 The classification of probability measures that satisfy both conformal invariance and domain Markov property is equivalent to characterizing solutions to the Belavin--Polyakov--Zamolodchikov (BPZ) equations, as established by Dubédat~[Dub07]. In this context, the partition functions for half-watermelon SLE and for multi-radial SLE serve as fundamental solutions to the BPZ equations. In this article, we investigate the large deviation principle for both half-watermelon SLE and multi-radial SLE. The associated rate function is given by the multi-time Loewner energy, introduced in~[CHPW26]. As applications, we provide an alternative proof of the large deviation principle for Dyson Brownian motion, as well as a new derivation of the boundary perturbation property of the multi-time Loewner energy. |
| title | Multi-time Loewner energy: rate function for large deviation |
| topic | Probability 60J67 |
| url | https://arxiv.org/abs/2602.20642 |