Language Evolution, Coalescent Processes, and the Consensus Problem on a Social Network

In recent times, there has been an increased interest in theories of language evolution that have an applicability to the study of dialect formation, linguistic change, creolization, the origin of language, and animal and robot communication systems in general. One particular question that has attracted some interest has the following general form: how might a group of linguistic agents arrive at a shared communication system purely through local patterns of interaction and without any global agency enforcing uniformity? In this paper, we consider a natural model of language (or more precisely, word) evolution on a social network, prove several theoretical properties, and establish connections to related phenomena in biology, social sciences, and physics.