Open Access
2013 Some results about ergodicity in shape for a crystal growth model
François Ezanno
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Electron. J. Probab. 18: 1-20 (2013). DOI: 10.1214/EJP.v18-2177


We study a crystal growth Markov model proposed by Gates and Westcott. This is an aggregation process where particles are packed in a square lattice accordingly to prescribed deposition rates. This model is parametrized by three values $(\beta_i, i=0,1,2)$ corresponding to depositions on three different types of sites. The main problem is to determine, for the shape of the crystal, when recurrence and when ergodicity do occur. Sufficient conditions are known both for ergodicity and transience. We establish some improved conditions and give a precise description of the asymptotic behavior in a special case. <br />


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François Ezanno. "Some results about ergodicity in shape for a crystal growth model." Electron. J. Probab. 18 1 - 20, 2013.


Accepted: 7 March 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1288.82057
MathSciNet: MR3035761
Digital Object Identifier: 10.1214/EJP.v18-2177

Primary: 60J27
Secondary: 60G55 , 60J10 , 60K25

Keywords: Markov chain , positive recurrence , random deposition

Vol.18 • 2013
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