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On the interaction of geometry, analysis and stochastics on a body
Author(s) -
Freiberg Uta R.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700610
Subject(s) - hausdorff dimension , brownian motion , mathematics , laplace operator , geometric analysis , dimension (graph theory) , motion (physics) , set (abstract data type) , geometry , natural (archaeology) , einstein , statistical physics , pure mathematics , physics , mathematical analysis , classical mechanics , computer science , mathematical physics , statistics , geology , differential algebraic equation , ordinary differential equation , paleontology , programming language , differential equation
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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