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We study stability of a growth process generated by sequential adsorption ofparticles on a one-dimensional lattice torus, that is, the process formed bythe numbers of adsorbed particles at lattice sites, called heights. Here thestability of process, loosely speaking, means that its components grow atapproximately the same rate. To assess stability quantitatively, we investigatethe stochastic process formed by differences of heights.  The model can be regarded as a variant of a Polya urn scheme with localgeometric interaction.

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