Abstract
We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We demonstrate the utility and computability of this measure by applying it to branched polymers, Brownian trees, and self-avoiding random walks.
ACKNOWLEDGMENTS
We would like to thank Tom Spencer and Jeremy Mason for useful conversations, and Benjamin Mann for his enthusiastic support. The Institute for Advanced Study and DARPA provided support for this project.
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