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May, 1993 Markov Models of Steady Crystal Growth
D. J. Gates, M. Westcott
Ann. Appl. Probab. 3(2): 339-355 (May, 1993). DOI: 10.1214/aoap/1177005427


We consider solid-on-solid models of two- and three-dimensional crystal growth described by Markov rate processes whose states are representations of the entire crystal surface and whose transitions are captures of single atoms by this surface or escapes of atoms. Under natural conditions on the transition probability rates, we prove ergodicity of the Markov process. This implies the existence of states of steady growth and statistically stationary surface structure. Microscopic surface instabilities do not therefore occur under such conditions. For two dimensions, our conditions are very general; for three dimensions, they are less general.


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D. J. Gates. M. Westcott. "Markov Models of Steady Crystal Growth." Ann. Appl. Probab. 3 (2) 339 - 355, May, 1993.


Published: May, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0779.60063
MathSciNet: MR1221155
Digital Object Identifier: 10.1214/aoap/1177005427

Primary: 60J20
Secondary: 82A60

Keywords: crystal growth , dynamic reversibility , Foster's theorem , Liapounov function , Markov process , polymer crystal

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.3 • No. 2 • May, 1993
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