Fluctuation and Dissipation on Fractals: A Probabilistic Approach
The analogies between the diffusion problem and the resistor network problem as witnessed by the Einstein relation have been very important for analytical and numerical investigations of linear problems in disordered geometries (e.g. percolating clusters)1. This raises the question whether the resistor problem can be identified in a purely probabilistic context. An affirmative answer has recently been given and it was shown that the Einstein relation follows from a simple probabilistic argument2,3. Here we present the results of a more general treatment.
KeywordsEinstein Relation Probabilistic Argument Homogeneous Markov Chain Resistor Problem Probabilistic Context
- for a review see e.g. the contributions of H.E. Stanley or A.Aharony in: Scaling Phenomena in Disordered Systems, R.Pynn and A.Skjeltorp, Plenum Press, New York 1985Google Scholar
- 2.R.Hilfer, Renormierungsansätze in der Theorie ungeordneter Systeme, Verlag Harri Deutsch, Frankfurt a.M. 1986Google Scholar
- 3.R. Hilfer and A. Blumen, preprintGoogle Scholar
- 5.R. Hilfer and A. Blumen, to be publishedGoogle Scholar