Mathematics of random growing interfaces

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Published 3 August 2001 • Published under licence by IOP Publishing Ltd
, , Citation Mathew D Penrose and J E Yukich 2001 J. Phys. A: Math. Gen. 34 6239 DOI 10.1088/0305-4470/34/32/303

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1 Department of Mathematical Sciences, University of Durham, South Road, Durham DH1 3LE, UK and Department of Mathematics, Lehigh University, Bethlehem PA 18015, USA

Dates

  1. Received 11 April 2001
  2. Published

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0305-4470/34/32/6239

Abstract

We establish a thermodynamic limit and Gaussian fluctuations for the height and surface width of the random interface formed by the deposition of particles on surfaces. The results hold for the standard ballistic deposition model as well as the surface relaxation model in the off-lattice setting. The results are proved with the aid of general limit theorems for stabilizing functionals of marked Poisson point processes.

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