Absence of geodesics in first-passage percolation on a half-plane

Jan Wehr, Jung Woo

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

An H-geodesic is a doubly infinite path which locally minimizes the passage time in the i.i.d. first passage percolation model on a half-plane H. Under the assumption that the bond passage times are continuously distributed with a finite mean, we prove that, with probability 1, H-geodesics do not exist. As a corollary we show that, with probability 1, any geodesic in the analogous model on the whole plane Z2 has to intersect all straight lines with rational slopes.

Original languageEnglish (US)
Pages (from-to)358-367
Number of pages10
JournalAnnals of Probability
Volume26
Issue number1
DOIs
StatePublished - Jan 1998

Keywords

  • Ergodicity
  • First-passage percolation
  • Infinite geodesics
  • Large deviation bounds
  • Time-minimizing paths

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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