  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.
