Restricting SLE(8/3) to an annulus

We study the probability that chordal $\text{SLE}_{8/3}$ in the unit disk from $\exp(ix)$ 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 one this probability decays like $\exp(-cx/(1-q))$ with $c=5\pi/8$ for $x\in[0,\pi]$. We also give a representation of this probability as a functional of a Legendre process.Comment: 28 pages, corrected proof of asymptotic dependenc

Letter from Ireland

Letter from Ireland is the first in a series of correspondence which our Editors hope to present regularly from foreign lands. A group of corresponding editors has been contacted to supply news and information thought to be of interest to our readers. We are happy to begin the new year with this Irish contribution