Large deviations of radial SLE$_{infty}$

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 ${phi_t^2 (zeta), dzeta}_{t in [0,1]}$ on the unit circle and equals $int_0^1 int_{S^1} |phi_t|^2/2,dzeta ,dt$. Our proof relies on the large deviation principle for the long-time average of the Brownian occupation measure by Donsker and Varadhan.