Dynamical aspects of Information Production Processes

Abstract

In this paper and talk we present a short proof of a theorem of Naranan stating that if sources grow exponentially and if items in sources also grow exponentially, then the system is Lotkaian, i.e. its size-frequency function is the law of Lotka.

We apply this technique to the case of power law growth of sources and of items in sources and determine the size- and rank frequency functions in this case. These functions have a greater variety of shapes than in the classical Naranan case and we give practical examples. We also show that, in this context, the law of Heaps can be proved. We also further generalise this technique to general growth models of sources and items in sources.