Absence of Phase Transition in Random Language Model.

Random Language Model is a simple model of human language, and, by studying the model, it is proposed that the emergence of order in language can be viewed as a phase transition. In the model, the process of sentence generation is expressed as a tree graph with nodes having symbols as variables. Theoretical analysis reveals that the distribution of symbols on a layer or a node of the tree follows a kind of Markov chains, strongly suggesting that no phase transition occurs. This is in contrast to previous studies, and indicates that the existence of phase transitions requires a complex model that cannot be reduced to a Markov chain.