A shape theorem for Riemannian first-passage percolation

T. LaGatta, J. Wehr

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

Riemannian first-passage percolation is a continuum model, with a distance function arising from a random Riemannian metric in Rd. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability of 1.

Original languageEnglish (US)
Article number024005JMP
JournalJournal of Mathematical Physics
Volume51
Issue number5
DOIs
StatePublished - May 1 2010

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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