Emergence of Zipf's law in the evolution of communication
Abstract
Zipf’s law seems to be ubiquitous in human languages and appears to be a universal property of complex communicating systems. Following the early proposal made by Zipf concerning the presence of a tension between the efforts of speaker and hearer in a communication system, we introduce evolution by means of a variational approach to the problem based on Kullback’s Minimum Discrimination of Information Principle. Therefore, using a formalism fully embedded in the framework of information theory, we demonstrate that Zipf’s law is the only expected outcome of an evolving communicative system under a rigorous definition of the communicative tension described by Zipf.
- Publication:
-
Physical Review E
- Pub Date:
- March 2011
- DOI:
- 10.1103/PhysRevE.83.036115
- arXiv:
- arXiv:1008.0938
- Bibcode:
- 2011PhRvE..83c6115C
- Keywords:
-
- 05.65.+b;
- 89.70.Hj;
- 87.23.Kg;
- 89.75.Da;
- Self-organized systems;
- Communication complexity;
- Dynamics of evolution;
- Systems obeying scaling laws;
- Nonlinear Sciences - Adaptation and Self-Organizing Systems;
- Condensed Matter - Statistical Mechanics;
- Computer Science - Information Theory;
- Mathematical Physics;
- Physics - Physics and Society
- E-Print:
- 7 pages, 2 figures