Multiradial Schramm-Loewner evolution: Infinite-time large deviations and transience

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Abuzaid, Osama, Healey, Vivian Olsiewski, Peltola, Eveliina
Format: Preprint
Published: 2026
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866918447438364672
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
id 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