ON THE CONTINUITY OF THE TIME CONSTANT OF FIRST-PASSAGE PERCOLATION.

J. Theodore Cox, Harry Kesten

Research output: Contribution to journalArticle

22 Scopus citations

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 languageEnglish (US)
Pages (from-to)809-819
Number of pages11
JournalJournal of Applied Probability
Volume18
Issue number4
DOIs
StatePublished - Jan 1 1981

ASJC Scopus subject areas

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

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