Restricting SLE(8/3) to an annulus

Abstract

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.

28 pages, corrected proof of asymptotic dependence

References in corpus (1)

• Critical percolation in annuli and $SL{E}_6$

Cited by in corpus (1)

• Stochastic geometry of critical curves, Schramm-Loewner evolutions, and conformal field theory