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Random walks on fractal structures and percolation clusters
Open accessAbstract
The notion of spectral dimensionality of a self-similar (fractal) structure is recalled, and its value for the family of Sierpinski gaskets derived via a scaling argument. Various random walk properties such as the probability of closed walks and the mean number of visited sites are shown to be governed by this spectral dimension. It is suggested that the number SN of distinct sites visited during an N-step random walk on an infinite cluster at percolation threshold varies asymptotically as : SN ∼ N2/3, in any dimension.
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Citations
Cited by
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
Bouchaud, J.-P., & Georges, A. (1990) · Physics Reports · doi:10.1016/0370-1573(90)90099-n · Cited by 4,162
Diffusion in regular and disordered lattices
Haus, J. W., & Kehr, K. W. (1987) · Physics Reports · doi:10.1016/0370-1573(87)90005-6 · Cited by 1,122
Physics of inhomogeneous inorganic materials
Nan, C.-W. (1993) · Progress in Materials Science · doi:10.1016/0079-6425(93)90004-5 · Cited by 1,050
Rammal, R., Toulouse, G., & Virasoro, M. A. (1986) · Reviews of Modern Physics · doi:10.1103/revmodphys.58.765 · Cited by 756
Self-citationAnimal movements and population dynamics in heterogeneous landscapes
Johnson, A. R., Wiens, J. A., Milne, B. T., & Crist, T. O. (1992) · Landscape Ecology · doi:10.1007/bf02573958 · Cited by 419
Metadata
- Authors
- Rammal, R., & Toulouse, G.
- Venue
- Journal de Physique Lettres
- Publisher
- EDP Sciences
- Published
- 1983
- Volume
- 44
- Issue
- 1
- Pages
- 13-22
- ISSN
- 0302-072X (ISSN-L)
- OpenAlex
- W2138085462
- Cited by
- 968
- References
- 0
- FWCI
- 95.18
- Type
- journal article
- Language
- en
- Open access
- green
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- Rammal, R., & Toulouse, G. (1983). Random walks on fractal structures and percolation clusters. Journal de Physique Lettres. https://doi.org/10.1051/jphyslet%3A0198300440101300
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