The Dimension of the Planar Brownian Frontier is 4/3
Probability
2008-11-26 v2 Mathematical Physics
math.MP
Abstract
In a series of recent preprints, we have proven that with probability one the Hausdorff dimension on the outer boundary of planar Brownian motion is 4/3, confirming a conjecture by Mandelbrot. It is also shown that the Hausdorff dimension of the set of cut points is a.s. 3/4. The present paper is an expository outline of the arguments involved in the proof of these and related results.
Cite
@article{arxiv.math/0010165,
title = {The Dimension of the Planar Brownian Frontier is 4/3},
author = {Gregory F. Lawler and Oded Schramm and Wendelin Werner},
journal= {arXiv preprint arXiv:math/0010165},
year = {2008}
}