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Percolation and epidemics (1957)

  • Nicolas Bacaër

Abstract

In 1957 Hammersley and Broadbent considered the propagation of a “fluid” in an infinite regular square network, where two neighbouring nodes are connected with a given probability. Among the possible examples, they mentioned the propagation of an epidemic in an orchard. They showed that there is critical probability below which no large epidemic can occur and above which large epidemics occur with a positive probability. Their article was the starting point of percolation theory.

Keywords

Monte Carlo Method Percolation Theory Royal Statistical Society Infected Tree Critical Probability 
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.

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Further reading

  1. 1.
    Grimmett, G., Welsh, D.: John Michael Hammersley. Biogr. Mem. Fellows R. Soc. 53, 163–183 (2007) CrossRefGoogle Scholar
  2. 2.
    Broadbent, S.R.: Discussion on symposium on Monte Carlo methods. J. R. Stat. Soc. B 16, 68 (1954) Google Scholar
  3. 3.
    Broadbent, S.R., Hammersley, J.M.: Percolation processes I: Crystals and mazes. Proc. Camb. Philos. Soc. 53, 629–641 (1957) MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Broadbent, T.: Simon Broadbent – The man with a sense of fun who gave advertising a value. Campaign, 26 April 2002. campaignlive.co.uk
  5. 5.
    Hammersley, J.M.: Percolation processes II: The connective constant. Proc. Camb. Philos. Soc. 53, 642–645 (1957) MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Hammersley, J.M.: Percolation processes: lower bounds for the critical probability. Ann. Math. Stat. 28, 790–795 (1957) MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Hammersley, J.M.: Origins of percolation theory. In: Deutscher, G., Zallen, R., Adler, J. (eds.) Percolation Structures and Processes, pp. 47–57. Israel Physical Society (1983) Google Scholar
  8. 8.
    Hammersley, J.M., Morton, K.W.: Poor man’s Monte Carlo. J. R. Stat. Soc. B 16, 23–38 (1954) MATHMathSciNetGoogle Scholar
  9. 9.
    Hammersley, J.M., Handscomb, D.C.: Monte Carlo Methods. Fletcher & Son, Norwich (1964). books.google.com MATHGoogle Scholar
  10. 10.
    Kesten, H.: The critical probability of bond percolation on the square lattice equals 1/2. Comm. Math. Phys. 74, 41–59 (1980) MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Metropolis, N., Ulam, S.: The Monte Carlo method. J. Amer. Stat. Assoc. 44, 335–341 (1949) MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.IRD (Institut de Recherche pour le Développement)BondyFrance

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