A growth model in multiple dimensions and the height of a random partial order

Details A growth model in multiple dimensions and the height of a random partial order A growth model in multiple dimensions and the height of a random partial order

2002-11-04

arxiv.org/abs/math/0211066v2

IMS Lecture Notes Monograph Series 2007, Vol. 55, 204-233

Mathematics

Probability

Published at http://dx.doi.org/10.1214/074921707000000373 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/p

Scientific paper

10.1214/074921707000000373

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.

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