We propose a theoretical model of random binary assemblies of discs wh
ich is the extension at any packing fraction of a model previously des
cribed by Dodds for dense packings. In dilute assemblies, the notion o
f contact between the grains must be replaced by that of neighbourhood
of the grains. We define the neighbours of a disc through the radical
tesselation. The model is tested on packings built grain after grain,
obtained from numerical simulations. Its results are then compared wi
th experimental results obtained on assemblies built on an air table :
this shows that the possibility of rearrangement in those assemblies
leads to segregation at a local scale.