Electronic Journal of Probability

Inhomogeneous first-passage percolation

Daniel Ahlberg, Michael Damron, and Vladas Sidoravicius

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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’.

Article information

Electron. J. Probab., Volume 21 (2016), paper no. 4, 19 pp.

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

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

inhomogeneous growth shape theorem columnar defect

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Ahlberg, Daniel; Damron, Michael; Sidoravicius, Vladas. Inhomogeneous first-passage percolation. Electron. J. Probab. 21 (2016), paper no. 4, 19 pp. doi:10.1214/16-EJP4412. https://projecteuclid.org/euclid.ejp/1454514664

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