A Shape Theorem for Riemannian First-Passage Percolation
Probability
2010-05-12 v3 Differential Geometry
Abstract
Riemannian first-passage percolation (FPP) is a continuum model, with a distance function arising from a random Riemannian metric in . 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.
Cite
@article{arxiv.0907.2228,
title = {A Shape Theorem for Riemannian First-Passage Percolation},
author = {Tom LaGatta and Jan Wehr},
journal= {arXiv preprint arXiv:0907.2228},
year = {2010}
}