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

TL;DR

This paper analyzes the stability of a one-dimensional lattice growth process with cooperative effects, focusing on the uniformity of growth rates through a stochastic process of height differences, akin to a local Polya urn model.

Contribution

It introduces a new variant of a Polya urn scheme with local geometric interactions to study growth stability in lattice models.

Findings

The process exhibits stability with heights growing at similar rates.

The height difference process can be characterized as a local Polya urn scheme.

Results provide insights into cooperative effects in lattice growth models.

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 Polya urn scheme with local geometric interaction.