Restricting SLE(8/3 ) to an annulus

We study the probability that chordal SLE 8 / 3 in the unit disk from exp ( i x ) to 1 avoids the disk of radius q centered at zero. We find the initial/boundary value problem satisfied by this probability as a function of x and a = ln q , and show that asymptotically as q tends to 1 this probability decays like exp ( − c x / ( 1 − q ) ) with c = 5 π / 8 for 0 < x ≤ π . We also give a representation of this probability as a multiplicative functional of a Legendre process.