On the interaction of geometry,analysis and stochastics on a body |
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| Authors: | Uta R. Freiberg |
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| Affiliation: | Mathematisches Institut, Fakultät für Mathematik und Informatik, Ernst-Abbé-Platz 2, DE-07743 Jena, Germany |
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| Abstract: | It is reasonable to expect that the geometrical feature of a body has influence to spectral asymptotics of its “natural” Laplacian as well as to the behavior of its “natural” Brownian motion. In fact, such an interaction can be expressed by a so–called “Einstein relation” implicating Hausdorff, spectral and walk dimension. These quantities express geometric, analytic and stochastic aspects of a set. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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