First-Passage Percolation, Subadditive Processes, Stochastic Networks, and Generalized Renewal Theory

  • J. M. Hammersley
  • D. J. A. Welsh


In 1957, Broadbent and Hammersley gave a mathematical formulation of percolation theory. Since then much work has been done in this field and has now led to first-passage percolation problems. In the following two examples we contrast the early formulation with its more recent developments.


Additive Process Percolation Theory Lateral Shift Renewal Theory Nonnegative Random Variable 
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Copyright information

© Springer-Verlag Berlin · Heidelberg 1965

Authors and Affiliations

  • J. M. Hammersley
    • 1
  • D. J. A. Welsh
    • 1
  1. 1.Oxford UniversityUK

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