Phase transitions in least-effort communications

Mikhail Prokopenko*, Nihat Ay, Oliver Obst, Daniel Polani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

We critically examine a model that attempts to explain the emergence of power laws (e.g., Zipf's law) in human language. The model is based on the principle of least effort in communications-specifically, the overall effort is balanced between the speaker effort and listener effort, with some trade-off. It has been shown that an information-theoretic interpretation of this principle is sufficiently rich to explain the emergence of Zipf's law in the vicinity of the transition between referentially useless systems (one signal for all referable objects) and indexical reference systems (one signal per object). The phase transition is defined in the space of communication accuracy (information content) expressed in terms of the trade-off parameter. Our study explicitly solves the continuous optimization problem, subsuming a recent, more specific result obtained within a discrete space. The obtained results contrast Zipf's law found by heuristic search (that attained only local minima) in the vicinity of the transition between referentially useless systems and indexical reference systems, with an inverse-factorial (sub-logarithmic) law found at the transition that corresponds to global minima. The inverse-factorial law is observed to be the most representative frequency distribution among optimal solutions.

Original languageEnglish
Article numberP11025
Pages (from-to)1-30
Number of pages30
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2010
Issue number11
DOIs
Publication statusPublished - Nov 2010
Externally publishedYes

Keywords

  • Communication
  • Exact results
  • Stochastic search
  • Supply and information networks

Fingerprint Dive into the research topics of 'Phase transitions in least-effort communications'. Together they form a unique fingerprint.

Cite this