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Percolation processes: I. Crystals and mazes

  • S. R. Broadbent (a1) and J. M. Hammersley (a2)
Abstract

The paper studies, in a general way, how the random properties of a ‘medium’ influence the percolation of a ‘fluid’ through it. The treatment diifers from conventional diffusion theory, in which it is the random properties of the fluid that matter. Fluid and medium bear general interpretations: for example, solute diffusing through solvent, electrons migrating over an atomic lattice, molecules penetrating a porous solid, disease infecting a community, etc.

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References
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(1)Good, I. J.The number of individuals in a cascade process. Proc. Camb. Phil. Soc. 45 (1949), 360–3.
(2)Hammersley, J. M.Markovian walks on crystals. Compos. math. 11 (1954), 171–86.
(3)Hammersley, J. M. and Morton, K. W.Poor man's Monte Carlo. J.R. Statist. Soc. B, 16 (1954), 2338.
(4)Hammersley, J. M.Percolation processes. II. The connective constant. Proc. Camb. Phil. Soc. 53 (1957), 642–5.
(5)Hammersley, J. M.Percolation processes. IV. Lower bounds for the critical probability. Ann. math. Statist (in the press).
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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