A Shape Theorem for Riemannian First-Passage Percolation

Details A Shape Theorem for Riemannian First-Passage Percolation A Shape Theorem for Riemannian First-Passage Percolation

2009-07-13

arxiv.org/abs/0907.2228v3

J.Math.Phys. 51, 053502 (2010)

Mathematics

Probability

Scientific paper

10.1063/1.3409344

Riemannian first-passage percolation (FPP) is a continuum model, with a distance function arising from a random Riemannian metric in $\R^d$. 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 one.

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