@article{ECP1517,
author = {Steven Lalley and Gregory Lawler and Hariharan Narayanan},
title = {Geometric Interpretation of Half-Plane Capacity},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {14},
year = {2009},
keywords = {Brownian motion, Schramm-Loewner Evolution},
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.},
pages = {no. 55, 566-571},
issn = {1083-589X},
doi = {10.1214/ECP.v14-1517},
url = {http://ecp.ejpecp.org/article/view/1517}}