%0 Journal Article
%T A Shape Theorem for Riemannian First-Passage Percolation
%A Tom LaGatta
%A Jan Wehr
%J Mathematics
%D 2009
%I arXiv
%R 10.1063/1.3409344
%X 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.
%U http://arxiv.org/abs/0907.2228v3