### 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) |
---|---|

Pages (from-to) | 1446-1486 |

Number of pages | 41 |

Journal | Annals of Applied Probability |

Volume | 29 |

Issue number | 3 |

DOIs | |

State | Published - 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

### Cite this

*Annals of Applied Probability*,

*29*(3), 1446-1486. https://doi.org/10.1214/18-AAP1414