Density fluctuations of assemblies of irreversibly deposited particles on solid surfaces

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Abstract
For general irreversible deposition processes, a relation between the variance σ2 of the number of deposited particles on subsystems out of a large surface and the available surface function Φ is obtained. This relation is based on a mean field assumption and follows the resolution of a master equation system. It is valid at low to intermediate values of the surface coverage θ as shown by comparison with exact results and with numerical simulations for special deposition models. In the low coverage limit, if the available surface function is written as a series expansion of the coverage θ, whose first nontrivial term varies as θk, the reduced variance has a similar expansion. However, the prefactor of θk derived in this article is in general different in both series expansions. This result has also been obtained by a rigorous argument based on the evolution of the k-particle distribution function with the coverage.