The Convergence of Markov Chains and Language

Abstract

Markov Chains are a category of stochastic processes with an associated dependence structure. Their inception resulted from A. A. Markov’s desire to disprove a rival’s assertion concerning the application of the Law of Large Numbers (LLN) to dependent variables. Markov’s use of a classic Russian novel to illustrate a dependent relationship between vowels and consonants serves as motivation for investigating the extent to which the properties of these processes can be applied to other means of communication. This work summarizes a history of the Law of Large Numbers and the Markovian properties associated with three different aspects of communication.