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

Jan Wehr, Jung Woo

Research output: Contribution to journalArticle

7 Citations (Scopus)

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 Z 2 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
StatePublished - Jan 1998

Fingerprint

First-passage Percolation
Half-plane
Geodesic
Passage Time
Intersect
Straight Line
Slope
Corollary
Minimise
Path
Model

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Absence of geodesics in first-passage percolation on a half-plane. / Wehr, Jan; Woo, Jung.

In: Annals of Probability, Vol. 26, No. 1, 01.1998, p. 358-367.

Research output: Contribution to journalArticle

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