# Geometric and Fractal Properties ofBrownian Motion and Random Walk Paths inTwo and Three

```@inproceedings{Lawler1998GeometricAF,
title={Geometric and Fractal Properties ofBrownian Motion and Random Walk Paths inTwo and Three},
author={D F Lawler},
year={1998}
}```
There is a close relationship between critical exponents for proa-bilities of events and fractal properties of paths of Brownian motion and random walk in two and three dimensions. Cone points, cut points, frontier points, and pioneer points for Brownian motion are examples of sets whose Hausdorr dimension can be given in terms of corresponding exponents. In the latter three cases, the exponents are examples of intersection exponents for Brownian motion. The \non-mean eld" or \multifractal… CONTINUE READING

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