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

作者：Shcherbakov Vadim; Volkov Stanislav^*

来源：Stochastic Processes and Their Applications, 2010, 120(6): 926-948.

DOI：10.1016/j.spa.2010.01.020

• Cooperative sequential adsorption
• Deposition
• Growth
• Urn models
• Reinforced random walks
• Lyapunov function

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 Polya urn scheme with local geometric interaction.

• 出版日期2010-6