### 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 |

### Fingerprint

### 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

**Approximating geodesics via random points.** / Davis, Erik; Sethuraman, Sunder.

Research output: Contribution to journal › Article

*Annals of Applied Probability*, vol. 29, no. 3, pp. 1446-1486. https://doi.org/10.1214/18-AAP1414

}

TY - JOUR

T1 - Approximating geodesics via random points

AU - Davis, Erik

AU - Sethuraman, Sunder

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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

AB - 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

KW - Consistency

KW - Distance

KW - Finsler

KW - Gamma convergence

KW - Geodesic

KW - Random geometric graph

KW - Scaling limit

KW - Shortest path

UR - http://www.scopus.com/inward/record.url?scp=85063357722&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063357722&partnerID=8YFLogxK

U2 - 10.1214/18-AAP1414

DO - 10.1214/18-AAP1414

M3 - Article

VL - 29

SP - 1446

EP - 1486

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 3

ER -