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 language | English (US) |
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Pages (from-to) | 469-474 |
Number of pages | 6 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 349 |
Issue number | 2 |
DOIs | |
State | Published - Jan 15 2009 |
Externally published | Yes |
Keywords
- Annulus
- Conformal restriction
- Elliptic functions
ASJC Scopus subject areas
- Analysis
- Applied Mathematics