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

Vadim Shcherbakov and Stanislav Volkov

Stochastic Processes and their Applications, 2010, vol. 120, issue 6, 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.

Keywords: Cooperative; sequential; adsorption; Deposition; Growth; Urn; models; Reinforced; random; walks; Lyapunov; function (search for similar items in EconPapers)
Date: 2010
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