How porous is the graph of Brownian motion?

Author:

Cox J. T.,Griffin Philip S.

Abstract

We prove that the graph of Brownian motion is almost surely porous, and determine the Hausdorff dimension of sets with a given porosity index. In particular we show that the porosity index of the graph is γ 0 0.6948 {\gamma _0} \doteq 0.6948 .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

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Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Assouad Dimension of Random Processes;Proceedings of the Edinburgh Mathematical Society;2018-11-16

2. Fractal Percolation, Porosity, and Dimension;Journal of Theoretical Probability;2016-04-28

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