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The Dimension of the Planar Brownian Frontier is 4/3

Gregory F. Lawler·Oded Schramm·Wendelin Werner
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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.

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Gregory F. Lawler, Oded Schramm, Wendelin Werner. 2000-10-18. The Dimension of the Planar Brownian Frontier is 4/3. https://arxiv.org/abs/math/0010165

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