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Asymptotics for First-Passage Times on Delaunay Triangulations

Published online by Cambridge University Press:  03 February 2011

LEANDRO P. R. PIMENTEL
Affiliation:
Institute of Mathematics, Federal University of Rio de Janeiro, Brazil (e-mail: leandro@im.ufrj.br)
Corresponding
E-mail address:

Abstract

In this paper we study planar first-passage percolation (FPP) models on random Delaunay triangulations. In [14], 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.

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Paper
Copyright
Copyright © Cambridge University Press 2011

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References

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