Brownian motion on a homogeneous random fractal |
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Authors: | B M Hambly |
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Institution: | (1) Statistical Laboratory, University of Cambridge, 16 Mill Lane, CB2 1SB Cambridge, UK |
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Abstract: | Summary We introduce a simple random fractal based on the Sierpinski gasket and construct a Brownian motion upon the fractal. The properties of the process on the Sierpinski gasket are modified by the random environment. A sample path construction of the process via time truncation is used, which is a direct construction of the process on the fractal from the associated Dirichlet forms. We obtain estimates on the resolvent and transition density for the process and hence a value for the spectral dimension which satisfiesd
s=2d
f/dw. A branching process in a random environment can be used to deduce some of the sample path properties of the process. |
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Keywords: | 60J60 60J25 60J65 |
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