An application of Jacobi's elliptic functions to asymptotic probabilities for conformal restriction measures

Details An application of Jacobi's elliptic functions to asymptotic probabilities for conformal restriction measures An application of Jacobi's elliptic functions to asymptotic probabilities for conformal restriction measures

2006-10-26

arxiv.org/abs/math/0610805v1

Mathematics

Probability

9 pages

Scientific paper

We show that for the conformal restriction measure with exponent $b$ in the
unit disk on hulls $\gamma$ connecting $e^{ix}$ to 1 the probability of the
event that $\gamma$ avoids the disk of radius $q$ centered at zero decays like
$\exp(-b\pi x/(1-q))$ if either $b\in[5/8,1]\cup[5/4,\infty)$ and
$x\in(0,\pi]$, or if $b\in(1,5/4)$, $x\in(0,\pi)$, and $bx\le\pi$.

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