Asymptotic probabilities for conformal restriction measures for an annulus

Robert O. Bauer

doi:10.1016/j.jmaa.2008.08.041

Asymptotic probabilities for conformal restriction measures for an annulus

Robert O. Bauer

Research output: Contribution to journal › Article › peer-review

Abstract

We show that for the conformal restriction measure with exponent b in the unit disk on hulls γ connecting e^{i 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 language	English (US)
Pages (from-to)	469-474
Number of pages	6
Journal	Journal of Mathematical Analysis and Applications
Volume	349
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2008.08.041
State	Published - Jan 15 2009
Externally published	Yes

Keywords

Annulus
Conformal restriction
Elliptic functions

ASJC Scopus subject areas

Analysis
Applied Mathematics

Online availability

10.1016/j.jmaa.2008.08.041

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AB - 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.

KW - Annulus

KW - Conformal restriction

KW - Elliptic functions

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ER -

Asymptotic probabilities for conformal restriction measures for an annulus

Abstract

Keywords

ASJC Scopus subject areas

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