Fluctuation and Dissipation on Fractals: A Probabilistic Approach

  • R. Hilfer
  • A. Blumen
Part of the NATO ASI Series book series (volume 167)


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.


Einstein Relation Probabilistic Argument Homogeneous Markov Chain Resistor Problem Probabilistic Context 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Y. Gefen, A. Aharony, S. Alexander, Phys.Rev.Lett. 50 (1983), 77ADSCrossRefGoogle Scholar
  2. C.K. Harris and R.B. Stinchcombe, Phys.Rev.Lett. 50 (1983), 1399MathSciNetADSCrossRefGoogle Scholar
  3. 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
  4. 2.
    R.Hilfer, Renormierungsansätze in der Theorie ungeordneter Systeme, Verlag Harri Deutsch, Frankfurt a.M. 1986Google Scholar
  5. 3.
    R. Hilfer and A. Blumen, preprintGoogle Scholar
  6. 4.
    K.L. Chung, Markov Chains, Springer, Berlin 1967MATHCrossRefGoogle Scholar
  7. 5.
    R. Hilfer and A. Blumen, to be publishedGoogle Scholar
  8. 6.
    E.B. Dynkin and A.A. Juschkewitsch, Markoffsche Prozesse, Springer, Berlin 1969CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • R. Hilfer
    • 1
  • A. Blumen
    • 2
  1. 1.Department of PhysicsUniversity of California, Los AngelesLos AngelesUSA
  2. 2.Physikalisches InstitutUniversität BayreuthBayreuthGermany (W.)

Personalised recommendations