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Restricting SLE(8/3) to an annulus

Robert O. Bauer
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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 $c=5π/8$ for $x\in[0,π]$. We also give a representation of this probability as a functional of a Legendre process.

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Robert O. Bauer. 2006-10-26. Restricting SLE(8/3) to an annulus. https://arxiv.org/abs/math/0602391

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