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

TL;DR

This paper extends large deviation principles for multiradial SLE$(ppa)$ curves from finite to infinite time, providing detailed escape probability estimates and proving transience for certain ppa values.

Contribution

It generalizes finite-time large deviation results to infinite time and derives new escape probability estimates for multiradial SLE curves.

Findings

Extended large deviation principle to infinite time for multiradial SLE

Established transience of SLE$(ppa)$ curves for ppa  8/3

Derived explicit asymptotics for Brownian loop measure interaction

Abstract

In previous work [AHP24], we proved a finite-time large deviation principle in the Hausdorff metric for multiradial Schramm-Loewner evolution, SLE$(\kappa)$, as $\kappa \to 0$, 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$(\kappa)$ curves in the common parameterization, which extend the single-curve estimates achieved in [AP26]. As a by-product, we also get that multiradial SLE$(\kappa)$ curves, with $\kappa \leq 8/3$, 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.