Geometric and Fractal Properties of Brownian Motion and Random Walk Paths in Two and Three Dimensions
نویسنده
چکیده
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" nature of Brownian paths can be seen in terms of the strict concavity of the intersection exponent. Random walk results can be obtained from Brownian motion results from strong approximation.
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