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Geometric Interpretation of Half-Plane Capacity

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Geometric Interpretation of Half-Plane Capacity
2.	Creator	Author's name, affiliation, country	Steven P. Lalley; University of Chicago; United States
2.	Creator	Author's name, affiliation, country	Gregory F. Lawler; University of Chicago; United States
2.	Creator	Author's name, affiliation, country	Hariharan Narayanan; MIT; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Brownian motion, Schramm-Loewner Evolution
3.	Subject	Subject classification	82B31
4.	Description	Abstract	Schramm-Loewner Evolution describes the scaling limits of interfaces in certain statistical mechanical systems. These interfaces are geometric objects that are not equipped with a canonical parametrization. The standard parametrization of SLE is via half-plane capacity, which is a conformal measure of the size of a set in the reference upper half-plane. This has useful harmonic and complex analytic properties and makes SLE a time-homogeneous Markov process on conformal maps. In this note, we show that the half-plane capacity of a hull $A$ is comparable up to multiplicative constants to more geometric quantities, namely the area of the union of all balls centered in $A$ tangent to $R$, and the (Euclidean) area of a $1$-neighborhood of $A$ with respect to the hyperbolic metric.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	NSF
7.	Date	(YYYY-MM-DD)	2009-12-21
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/1517
10.	Identifier	Digital Object Identifier	10.1214/ECP.v14-1517
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 14
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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