### 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) |
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Article number | 024005JMP |

Journal | Journal of Mathematical Physics |

Volume | 51 |

Issue number | 5 |

DOIs | |

State | Published - May 2010 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

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

**A shape theorem for Riemannian first-passage percolation.** / LaGatta, T.; Wehr, Jan.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 51, no. 5, 024005JMP. https://doi.org/10.1063/1.3409344

}

TY - JOUR

T1 - A shape theorem for Riemannian first-passage percolation

AU - LaGatta, T.

AU - Wehr, Jan

PY - 2010/5

Y1 - 2010/5

N2 - 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.

AB - 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.

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U2 - 10.1063/1.3409344

DO - 10.1063/1.3409344

M3 - Article

AN - SCOPUS:77955252488

VL - 51

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 5

M1 - 024005JMP

ER -