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The Dimension of the Frontier of Planar Brownian Motion

   
@article{ECP975,
	author = {Gregory Lawler},
	title = {The Dimension of the Frontier of Planar Brownian Motion},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {1},
	year = {1996},
	keywords = {Brownian motion, Hausdorff dimension, frontier, random fractals},
	abstract = {Let $B$ be a two dimensional Brownian motion and let the frontier of $B[0,1]$ be defined as the set of all points in $B[0,1]$ that are in the closure of the unbounded connected component of its complement. We prove that the Hausdorff dimension of the frontier equals $2(1 - \alpha)$ where $\alpha$ is an exponent for Brownian motion called the two-sided disconnection exponent. In particular, using an estimate on $\alpha$ due to Werner, the Hausdorff dimension is greater than $1.015$.},
	pages = {no. 5, 29-47},
	issn = {1083-589X},
	doi = {10.1214/ECP.v1-975},    
        url = {http://ecp.ejpecp.org/article/view/975}}