Strict Concavity of the Intersection Exponent for Brownian Motion in Two and Three Dimensions
نویسنده
چکیده
The intersection exponent for Brownian motion is a measure of how likely Brownian motion paths in two and three dimensions do not intersect. We consider the intersection exponent () = d (k;) as a function of and show that has a continuous, negative second derivative. As a consequence, we improve some estimates for the intersection exponent; in particular, we give the rst proof that the intersection exponent 3 (1; 1) is strictly greater than the mean eld prediction. The results here are used in a later paper to analyze the multifractal spectrum of the harmonic measure of Brownian motion paths.
منابع مشابه
Geometric and Fractal Properties of Brownian Motion and Random Walk Paths in Two and Three Dimensions
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 exponent...
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