A shape theorem for Riemannian first-passage percolation

T. LaGatta, Jan Wehr

Research output: Contribution to journal › Article

5 Citations (Scopus)

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 2010

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First-passage Percolation
Riemannian Metric
theorems
Rescaling
Continuum Model
Distance Function
Theorem
balls
Ball
continuums
Converge
Metric
Model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

A shape theorem for Riemannian first-passage percolation. / LaGatta, T.; Wehr, Jan.

In: Journal of Mathematical Physics, Vol. 51, No. 5, 024005JMP, 05.2010.

Research output: Contribution to journal › Article

LaGatta, T & Wehr, J 2010, 'A shape theorem for Riemannian first-passage percolation', Journal of Mathematical Physics, vol. 51, no. 5, 024005JMP. https://doi.org/10.1063/1.3409344
LaGatta T, Wehr J. A shape theorem for Riemannian first-passage percolation. Journal of Mathematical Physics. 2010 May;51(5). 024005JMP. https://doi.org/10.1063/1.3409344
LaGatta, T. ; Wehr, Jan. / A shape theorem for Riemannian first-passage percolation. In: Journal of Mathematical Physics. 2010 ; Vol. 51, No. 5.
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