### Abstract

Let U be the distribution function of the non-negative passage time of an individual edge of the square lattice, and let a//o//n be the minimal passage time from (0,0) to (n,0). The process a//o//n/n converges in probability as n approaches infinity to a finite constant mu (U) called the time constant. It is proved that mu (U//k)approaches mu (U) whenever U//k converges weakly to U.

Original language | English (US) |
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Pages (from-to) | 809-819 |

Number of pages | 11 |

Journal | Journal of Applied Probability |

Volume | 18 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1981 |

### ASJC Scopus subject areas

- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty

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## Cite this

Cox, J. T., & Kesten, H. (1981). ON THE CONTINUITY OF THE TIME CONSTANT OF FIRST-PASSAGE PERCOLATION.

*Journal of Applied Probability*,*18*(4), 809-819. https://doi.org/10.1017/S0021900200034161