Gaussian fields and random packing

Yu. Baryshnikov, J. E. Yukich

Published 2002-02-07Version 1

Consider sequential packing of unit balls in a large cube, as in the Renyi car-parking model, but in any dimension and with Poisson input. We show after suitable rescaling that the spatial distribution of packed balls tends to that of a Gaussian field in the thermodynamic limit. We prove analogous results for related applied models, including ballistic deposition and spatial birth-growth models.