Escape probability and transience for SLE
  We give estimates for the probability that a chordal, radial or two-sided radial SLE$_\kappa$ curve retreats far from its terminal point after coming close to it, for $\kappa \leq 4$. The estimates are uniform over all initial segments of the curve, and are sharp up to a universal constant. 
Laurence S. Field, Gregory F. Lawler
math.PR