Screw it.  I was going to make a more detailed piece, but this will have to do for now.

Cultural transmission is more similar to a weighted, directed graph than to some other models.

We can think of agents as the nodes, and their modes of interaction and communication as the edges.

Cultural norms reinforce themselves through interactions and use, creating an environment where they are dominant.

Key for assimilation is cultural pressure to conform.  If all interactions are with the host culture, the pressure to conform is enormous and there is no reinforcement to support resisting it.

This is partially based on the dispersal of agents and their interactions within the environment, but it is also based on relative size.

Any given nation therefore has both a maximum theoretical and a practical assimilatory capacity.  This can be altered by a number of factors, including policy, dominant ideology, and geographical and cultural distribution.

Of course, in the modern world, the number of potential cultural transmission vectors is much larger (particularly including the Internet).