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 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics