Restricting SLE(8/3) to an annulus
We study the probability that chordal $\text{SLE}_{8/3}$ in the unit disk from $\exp(ix)$ to 1 avoids the disk of radius $q$ centered at zero. We find the initial/boundary-value problem satisfied by this probability as a function of $x$ and $a=\ln q$, and show that asymptotically as $q$ tends to one...
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| creator | Bauer, Robert O |
| description | We study the probability that chordal $\text{SLE}_{8/3}$ in the unit disk
from $\exp(ix)$ to 1 avoids the disk of radius $q$ centered at zero. We find
the initial/boundary-value problem satisfied by this probability as a function
of $x$ and $a=\ln q$, and show that asymptotically as $q$ tends to one this
probability decays like $\exp(-cx/(1-q))$ with $c=5\pi/8$ for $x\in[0,\pi]$. We
also give a representation of this probability as a functional of a Legendre
process. |
| doi_str_mv | 10.48550/arxiv.math/0602391 |
| format | Article |
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from $\exp(ix)$ to 1 avoids the disk of radius $q$ centered at zero. We find
the initial/boundary-value problem satisfied by this probability as a function
of $x$ and $a=\ln q$, and show that asymptotically as $q$ tends to one this
probability decays like $\exp(-cx/(1-q))$ with $c=5\pi/8$ for $x\in[0,\pi]$. We
also give a representation of this probability as a functional of a Legendre
process.</description><identifier>DOI: 10.48550/arxiv.math/0602391</identifier><language>eng</language><subject>Mathematics - Complex Variables ; Mathematics - Probability</subject><creationdate>2006-02</creationdate><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/math/0602391$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.math/0602391$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Bauer, Robert O</creatorcontrib><title>Restricting SLE(8/3) to an annulus</title><description>We study the probability that chordal $\text{SLE}_{8/3}$ in the unit disk
from $\exp(ix)$ to 1 avoids the disk of radius $q$ centered at zero. We find
the initial/boundary-value problem satisfied by this probability as a function
of $x$ and $a=\ln q$, and show that asymptotically as $q$ tends to one this
probability decays like $\exp(-cx/(1-q))$ with $c=5\pi/8$ for $x\in[0,\pi]$. We
also give a representation of this probability as a functional of a Legendre
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from $\exp(ix)$ to 1 avoids the disk of radius $q$ centered at zero. We find
the initial/boundary-value problem satisfied by this probability as a function
of $x$ and $a=\ln q$, and show that asymptotically as $q$ tends to one this
probability decays like $\exp(-cx/(1-q))$ with $c=5\pi/8$ for $x\in[0,\pi]$. We
also give a representation of this probability as a functional of a Legendre
process.</abstract><doi>10.48550/arxiv.math/0602391</doi><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| subjects | Mathematics - Complex Variables Mathematics - Probability |
| title | Restricting SLE(8/3) to an annulus |
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