Multiradial Schramm-Loewner evolution: Infinite-time large deviations and transience
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| Format: | Preprint |
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2026
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| _version_ | 1866918447438364672 |
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| author | Abuzaid, Osama Healey, Vivian Olsiewski Peltola, Eveliina |
| author_facet | Abuzaid, Osama Healey, Vivian Olsiewski Peltola, Eveliina |
| contents | In previous work [AHP24], we proved a finite-time large deviation principle in the Hausdorff metric for multiradial Schramm-Loewner evolution, SLE$(κ)$, as $κ\to 0$, with good rate function being the multiradial Loewner energy. Here, we extend this result to infinite time in the topology of common-capacity-parameterized curves, and streamline the proof. A main step is to derive detailed escape probability estimates for multiradial SLE$(κ)$ curves in the common parameterization, which extend the single-curve estimates achieved in [AP26]. As a by-product, we also get that multiradial SLE$(κ)$ curves, with $κ\leq 8/3$, are transient at their common terminal point, generalizing [FL15, HL21]. As a corollary to the LDP result, we obtain explicit asymptotics of the Brownian loop measure interaction term for finite-energy radial multichords, which is linear in the capacity-time and coincides with a certain choice of a cocycle for the Virasoro algebra. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_13387 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multiradial Schramm-Loewner evolution: Infinite-time large deviations and transience Abuzaid, Osama Healey, Vivian Olsiewski Peltola, Eveliina Probability Mathematical Physics In previous work [AHP24], we proved a finite-time large deviation principle in the Hausdorff metric for multiradial Schramm-Loewner evolution, SLE$(κ)$, as $κ\to 0$, with good rate function being the multiradial Loewner energy. Here, we extend this result to infinite time in the topology of common-capacity-parameterized curves, and streamline the proof. A main step is to derive detailed escape probability estimates for multiradial SLE$(κ)$ curves in the common parameterization, which extend the single-curve estimates achieved in [AP26]. As a by-product, we also get that multiradial SLE$(κ)$ curves, with $κ\leq 8/3$, are transient at their common terminal point, generalizing [FL15, HL21]. As a corollary to the LDP result, we obtain explicit asymptotics of the Brownian loop measure interaction term for finite-energy radial multichords, which is linear in the capacity-time and coincides with a certain choice of a cocycle for the Virasoro algebra. |
| title | Multiradial Schramm-Loewner evolution: Infinite-time large deviations and transience |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2604.13387 |