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Some results about ergodicity in shape for a crystal growth model


 
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1. Title Title of document Some results about ergodicity in shape for a crystal growth model
 
2. Creator Author's name, affiliation, country François Ezanno; Aix-Marseille Université; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Markov chain; random deposition; positive recurrence
 
3. Subject Subject classification 60J27; 60G55; 60K25; 60J10
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 2013-03-07
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2177
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2177
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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