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VOL. 55 | 2007 A growth model in multiple dimensions and the height of a random partial order
Timo Seppäläinen

Editor(s) Eric A. Cator, Geurt Jongbloed, Cor Kraaikamp, Hendrik P. Lopuhaä, Jon A. Wellner


We introduce a model of a randomly growing interface in multidimensional Euclidean space. The growth model incorporates a random order model as an ingredient of its graphical construction, in a way that replicates the connection between the planar increasing sequences model and the one-dimensional Hammersley process. We prove a hydrodynamic limit for the height process, and a limit which says that certain perturbations of the random surface follow the characteristics of the macroscopic equation. By virtue of the space-time Poissonian construction, we know the macroscopic velocity function explicitly up to a constant factor.


Published: 1 January 2007
First available in Project Euclid: 4 December 2007

zbMATH: 1181.60149
MathSciNet: MR2459941

Digital Object Identifier: 10.1214/074921707000000373

Primary: 60K35
Secondary: 82C22

Rights: Copyright © 2007, Institute of Mathematical Statistics


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