Coloured Random Graphs, Simple Random Allocation of Coloured Balls into Coloured Bins

Abstract

Simple coloured random allocation model is obtained when coloured balls are sequentially inserted at random into coloured bins. The empirical occupancy measure of the simple coloured random allocation model counts the number of bins of a given colour with a given number of balls of each colour. In this paper we show that, given the colours, both the empirical occupancy measure of simple coloured random allocation models and the empirical neighbourhood distribution of sparse coloured random graph models converge weakly to the product of independent Poisson distributions.