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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