We derive the large deviation principle for radial Schramm-Loewner evolution ($\operatorname{ SLE}$) on the unit disk with parameter $\kappa \rightarrow \infty$. 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 $\{ \phi_t^2 (\zeta)\, d\zeta\}_{ t \in [0,1]}$ on the unit circle and equals $\int_0^1 \int_{ S^1} |\phi_t'|^2/2\,d\zeta \,dt$. Our proof relies on the large deviation principle for the long-time average of the Brownian occupation measure by Donsker and Varadhan.
Categories: math.PR math.CV