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1 results

  • Weak moment conditions for time coordinates in first-passage percolation models

  • John C. Wierman
  • Journal:
    Journal of Applied Probability / Volume 17 / Issue 4 / December 1980
    Published online by Cambridge University Press:
    14 July 2016, pp. 968-978
    Print publication:
    December 1980

  • A generalization of first-passage percolation theory proves that the fundamental convergence theorems hold provided only that the time coordinate distribution has a finite moment of a positive order. The existence of a time constant is proved by considering first-passage times between intervals of sites, rather than the usual point-to-point and point-to-line first-passage times. The basic limit theorems for the related stochastic processes follow easily by previous techniques. The time constant is evaluated as 0 when the atom at 0 of the time-coordinate distribution exceeds½.