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2016 Inhomogeneous first-passage percolation
Daniel Ahlberg, Michael Damron, Vladas Sidoravicius
Electron. J. Probab. 21: 1-19 (2016). DOI: 10.1214/16-EJP4412

Abstract

We study first-passage percolation where edges in the left and right half-planes are assigned values according to different distributions. We show that the asymptotic growth of the resulting inhomogeneous first-passage process obeys a shape theorem, and we express the limiting shape in terms of the limiting shapes for the homogeneous processes for the two weight distributions. We further show that there exist pairs of distributions for which the rate of growth in the vertical direction is strictly larger than the rate of growth of the homogeneous process with either of the two distributions, and that this corresponds to the creation of a defect along the vertical axis in the form of a ‘pyramid’.

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Daniel Ahlberg. Michael Damron. Vladas Sidoravicius. "Inhomogeneous first-passage percolation." Electron. J. Probab. 21 1 - 19, 2016. https://doi.org/10.1214/16-EJP4412

Information

Received: 7 July 2015; Accepted: 9 November 2015; Published: 2016
First available in Project Euclid: 3 February 2016

zbMATH: 1338.60225
MathSciNet: MR3485346
Digital Object Identifier: 10.1214/16-EJP4412

Subjects:
Primary: 60K35

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