Asymptotic probabilities for conformal restriction measures for an annulus

Robert O. Bauer

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We show that for the conformal restriction measure with exponent b in the unit disk on hulls γ connecting ei x to 1 the probability of the event that γ avoids the disk of radius q centered at zero decays like exp (- b π x / (1 - q)) if either b ∈ [5 / 8, 1] ∪ [5 / 4, ∞) and x ∈ (0, π], or if b ∈ (1, 5 / 4), x ∈ (0, π), and b x ≤ π.

    Original languageEnglish (US)
    Pages (from-to)469-474
    Number of pages6
    JournalJournal of Mathematical Analysis and Applications
    Volume349
    Issue number2
    DOIs
    StatePublished - Jan 15 2009

    Keywords

    • Annulus
    • Conformal restriction
    • Elliptic functions

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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