Large deviations of radial SLE${}_{\infty }$

Abstract

We derive the large deviation principle for radial Schramm-Loewner evolution ($\mathrm{SLE}$) on the unit disk with parameter $\kappa \to \infty$. Restricting to the time interval $[0,1]$, the good rate function is finite only on a certain family of Loewner chains driven by absolutely continuous probability measures $\{{\varphi }_t^2(\zeta )d\zeta {\}}_{t\in [0,1]}$ on the unit circle and equals ${\int }_0^1{\int }_{S^1}|{\varphi }_t^{\prime }{|}^2/2d\zeta dt$. Our proof relies on the large deviation principle for the long-time average of the Brownian occupation measure by Donsker and Varadhan.

arXiv comment17 pages, 1 figure, revised according to referee's report

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• Duality of Chordal SLE
• Quantum Loewner Evolution
• Equivalent Descriptions of the Loewner Energy
• Scaling limits of anisotropic Hastings-Levitov clusters
• The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE${}_{0+}$
• The Loewner energy of loops and regularity of driving functions
• Interplay between Loewner and Dirichlet energies via conformal welding and flow-lines

Cited by in corpus (2)

• Large deviations of Schramm-Loewner evolutions: A survey
• Two-loop Loewner potentials