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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
LEANDRO P. R. PIMENTEL*
Affiliation:
Institute of Mathematics, Federal University of Rio de Janeiro, Brazil (e-mail: leandro@im.ufrj.br)
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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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Type
Paper
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Combinatorics, Probability and Computing , Volume 20 , Issue 3 , May 2011 , pp. 435 - 453
Copyright
Copyright © Cambridge University Press 2011

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