Published online by Cambridge University Press: 03 February 2011
In this paper we study planar first-passage percolation (FPP) models on random Delaunay triangulations. In , Vahidi-Asl and Wierman showed, using sub-additivity theory, that the rescaled first-passage time converges to a finite and non-negative constant μ. We show a sufficient condition to ensure that μ>0 and derive some upper bounds for fluctuations. Our proofs are based on percolation ideas and on the method of martingales with bounded increments.