SLE intersecting with random hulls

Abstract Lawler, Schramm, and Werner gave in 2003 an explicit formula of the probability that SLE ( 8 / 3 ) does not intersect a deterministic hull. For general SLE ( κ ) with κ ≠ 8 / 3 , no such explicit formula has been obtained so far. In this paper, we shall consider a random hull generated by an independent chordal conformal restriction measure and obtain an explicit formula for the probability that SLE ( κ ) does not intersect this random hull for any κ ∈ ( 0 , 8 ) . As a corollary, we will give a new proof of Werner's result on conformal restriction measures.