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Intersection probabilities for a chordal SLE path and a semicircle

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Intersection probabilities for a chordal SLE path and a semicircle
2.	Creator	Author's name, affiliation, country	Tom Alberts; New York University
2.	Creator	Author's name, affiliation, country	Michael J Kozdron; University of Regina
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Schramm-Loewner evolution; restriction property; Hausdorff dimension; swallowing time; intersection probability; Schwarz-Christoffel transformation
3.	Subject	Subject classification	82B21; 60K35; 60G99; 60J65
4.	Description	Abstract	We derive a number of estimates for the probability that a chordal SLE$_\kappa$ path in the upper half plane $\mathbb{H}$ intersects a semicircle centred on the real line. We prove that if $0<\kappa <8$ and $\gamma:[0,\infty) \to \overline{\mathbb{H}}$ is a chordal SLE$_\kappa$ in $\mathbb{H}$ from $0$ to $\infty$, then $P\{\gamma[0,\infty) \cap \mathcal{C}(x;rx) \neq \emptyset\} \asymp r^{4a-1}$ where $a=2/\kappa$ and $\mathcal{C}(x;rx)$ denotes the semicircle centred at $x>0$ of radius $rx$, $00$. For $4<\kappa<8$, we also estimate the probability that an entire semicircle on the real line is swallowed at once by a chordal SLE$_\kappa$ path in $\mathbb{H}$ from $0$ to $\infty$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Natural Sciences and Engineering Research Council (NSERC) of Canada
7.	Date	(YYYY-MM-DD)	2008-08-14
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1399
10.	Identifier	Digital Object Identifier	10.1214/ECP.v13-1399
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 13
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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