Approximating geodesics via random points

Erik Davis, Sunder Sethuraman

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Given a cost functional F on paths γ in a domain D ⊂ R d , in the form F(γ) = 0 1 f (γ (t), γ (t))dt, it is of interest to approximate its minimum cost and geodesic paths. Let X 1 , . . ., X n be points drawn independently from D according to a distribution with a density. Form a random geometric graph on the points where X i and X j are connected when 0 < |X i − X j

Original languageEnglish (US)
Pages (from-to)1446-1486
Number of pages41
JournalAnnals of Applied Probability
Volume29
Issue number3
DOIs
StatePublished - Jan 1 2019

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Keywords

  • Consistency
  • Distance
  • Finsler
  • Gamma convergence
  • Geodesic
  • Random geometric graph
  • Scaling limit
  • Shortest path

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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