Restricting SLE(8/3) to an annulus

2006/02/17 by Robert O. Bauer, Bauer, Robert O. · 1 citation
Mathematics · #60H30 #60K35 #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.CV #math.PR #msc:60H30 #msc:60K35

paper · pdf · doi:10.48550/arxiv.math/0602391

28 pages, corrected proof of asymptotic dependence

openalex publication_date 2006/02/17 · arxiv created 2006/10/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the probability that chordal 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∈[0,π]. We also give a representation of this probability as a functional of a Legendre process.

Cited by

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

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