# Approximating geodesics via random points

Erik Davis, Sunder Sethuraman

Research output: Contribution to journalArticle

### 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 language English (US) 1446-1486 41 Annals of Applied Probability 29 3 https://doi.org/10.1214/18-AAP1414 Published - Jan 1 2019

### Fingerprint

Geodesic
Random Geometric Graph
Path
Costs
Research and Development
Form
Graph

### 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

### Cite this

In: Annals of Applied Probability, Vol. 29, No. 3, 01.01.2019, p. 1446-1486.

Research output: Contribution to journalArticle

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