Diffusion in sparse networks: Linear to semilinear crossover

Yaron De Leeuw, Doron Cohen

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We consider random networks whose dynamics is described by a rate equation, with transition rates wnm that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient D. In one dimension it is well known that D can display an abrupt percolation-like transition from diffusion (D>0) to subdiffusion (D=0). A question arises whether such a transition happens in higher dimensions. Numerically D can be evaluated using a resistor network calculation, or optionally it can be deduced from the spectral properties of the system. Contrary to a recent expectation that is based on a renormalization-group analysis, we deduce that D is finite, suggest an "effective-range-hopping" procedure to evaluate it, and contrast the results with the linear estimate. The same approach is useful in the analysis of networks that are described by quasi-one-dimensional sparse banded matrices.

Original languageEnglish
Article number051120
JournalPhysical Review E
Issue number5
StatePublished - 19 Nov 2012

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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