Geodesics in two-dimensional first-passage percolation

Cristina Licea, Charles M. Newman

Research output: Contribution to journalArticlepeer-review

Abstract

We consider standard first-passage percolation on ℤ2. Geodesics are nearest-neighbor paths in ℤ2, each of whose segments is time-minimizing. We prove part of the conjecture that doubly infinite geodesics do not exist. Our main tool is a result of independent interest about the coalescing of semi-infinite geodesics.

Original languageEnglish (US)
Pages (from-to)399-410
Number of pages12
JournalAnnals of Probability
Volume24
Issue number1
DOIs
StatePublished - 1996

Keywords

  • Disordered Ising model
  • First-passage percolation
  • Geodesic
  • Random metric

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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