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arXiv · 0907.2228

A Shape Theorem for Riemannian First-Passage Percolation

Tom LaGatta·Jan Wehr
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Abstract

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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Tom LaGatta, Jan Wehr. 2010-04-09. A Shape Theorem for Riemannian First-Passage Percolation. https://doi.org/10.1063/1.3409344

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