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Transition densities for Brownian motion on the Sierpinski carpet. (English) Zbl 0739.60071
Upper and lower bounds are obtained for the transition densities \(p(t,x,y)\) of Brownian motion on the Sierpinski carpet. These are of the same form as those which hold for the Sierpinski gasket. In addition, the joint continuity of \(p(t,x,y)\) is proved, the existence of the spectral dimension is established, and the Einstein relation, connecting the spectral dimension, the Hausdorff dimension and the resistance exponent is shown to hold.

60J65 Brownian motion
60K35 Interacting random processes; statistical mechanics type models; percolation theory
Full Text: DOI
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