A large deviation principle for the Schramm-Loewner evolution in the uniform topology

TL;DR

This paper proves a large deviation principle for chordal SLE$_ppa$ curves as ppa approaches zero, showing the rate function equals the Loewner energy, in the uniform topology, strengthening previous Hausdorff topology results.

Contribution

It establishes a large deviation principle for SLE curves in the uniform topology, linking the rate function to the Loewner energy, and extends prior work from Hausdorff to uniform topology.

Findings

Large deviation principle for SLE in uniform topology

Rate function equals Loewner energy of the curve

Strengthens previous results using Hausdorff topology

Abstract

We establish a large deviation principle for chordal SLE$_\kappa$ parametrized by capacity, as the parameter $\kappa \to 0+$, in the topology generated by uniform convergence on compact intervals of the positive real line. The rate function is shown to equal the Loewner energy of the curve. This strengthens the recent result of E. Peltola and Y. Wang who obtained the analogous statement using the Hausdorff topology.