Zipf's law from a communicative phase transition

R. Ferrer i Cancho ()

The European Physical Journal B: Condensed Matter and Complex Systems, 2005, vol. 47, issue 3, 449-457

Abstract: Here we present a new model for Zipf's law in human word frequencies. The model defines the goal and the cost of communication using information theory. The model shows a continuous phase transition from a no communication to a perfect communication phase. Scaling consistent with Zipf's law is found in the boundary between phases. The exponents are consistent with minimizing the entropy of words. The model differs from a previous model [Ferrer i Cancho, Solé, Proc. Natl. Acad. Sci. USA 100, 788–791 (2003)] in two aspects. First, it assumes that the probability of experiencing a certain stimulus is controlled by the internal structure of the communication system rather than by the probability of experiencing it in the `outside' world, which makes it specially suitable for the speech of schizophrenics. Second, the exponent α predicted for the frequency versus rank distribution is in a range where α>1, which may explain that of some schizophrenics and some children, with α=1.5-1.6. Among the many models for Zipf's law, none explains Zipf's law for that particular range of exponents. In particular, two simplistic models fail to explain that particular range of exponents: intermittent silence and Simon's model. We support that Zipf's law in a communication system may maximize the information transfer under constraints. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Date: 2005
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1140/epjb/e2005-00340-y (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:47:y:2005:i:3:p:449-457

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/e2005-00340-y

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().