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Stability of a growth process generated by monomer filling with nearest-neighbor cooperative effects

Shcherbakov, Vadim and Volkov, Stanislav LU (2010) In Stochastic Processes and their Applications 120(6). p.926-948
Abstract
We study stability of a growth process generated by sequential adsorption of particles on a one-dimensional lattice torus, that is, the process formed by the numbers of adsorbed particles at lattice sites, called heights. Here the stability of process, loosely speaking, means that its components grow at approximately the same rate. To assess stability quantitatively, we investigate the stochastic process formed by differences of heights.



The model can be regarded as a variant of a Pólya urn scheme with local geometric interaction.
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Cooperative sequential adsorption, Deposition, Growth, Urn models, Reinforced random walks, Lyapunov function
in
Stochastic Processes and their Applications
volume
120
issue
6
pages
926 - 948
publisher
Elsevier
external identifiers
  • scopus:77950593843
ISSN
1879-209X
DOI
10.1016/j.spa.2010.01.020
language
English
LU publication?
no
id
e6caef92-6827-4b73-a17a-5d6751ccaafa (old id 4359871)
date added to LUP
2014-03-17 15:05:18
date last changed
2018-06-10 03:27:09
@article{e6caef92-6827-4b73-a17a-5d6751ccaafa,
  abstract     = {We study stability of a growth process generated by sequential adsorption of particles on a one-dimensional lattice torus, that is, the process formed by the numbers of adsorbed particles at lattice sites, called heights. Here the stability of process, loosely speaking, means that its components grow at approximately the same rate. To assess stability quantitatively, we investigate the stochastic process formed by differences of heights.<br/><br>
<br/><br>
The model can be regarded as a variant of a Pólya urn scheme with local geometric interaction.},
  author       = {Shcherbakov, Vadim and Volkov, Stanislav},
  issn         = {1879-209X},
  keyword      = {Cooperative sequential adsorption,Deposition,Growth,Urn models,Reinforced random walks,Lyapunov function},
  language     = {eng},
  number       = {6},
  pages        = {926--948},
  publisher    = {Elsevier},
  series       = {Stochastic Processes and their Applications},
  title        = {Stability of a growth process generated by monomer filling with nearest-neighbor cooperative effects},
  url          = {http://dx.doi.org/10.1016/j.spa.2010.01.020},
  volume       = {120},
  year         = {2010},
}