### 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 language | English (US) |
---|---|

Article number | 024005JMP |

Journal | Journal of Mathematical Physics |

Volume | 51 |

Issue number | 5 |

DOIs | |

State | Published - May 1 2010 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

## Fingerprint Dive into the research topics of 'A shape theorem for Riemannian first-passage percolation'. Together they form a unique fingerprint.

## Cite this

LaGatta, T., & Wehr, J. (2010). A shape theorem for Riemannian first-passage percolation.

*Journal of Mathematical Physics*,*51*(5), [024005JMP]. https://doi.org/10.1063/1.3409344