A critical analysis of a model for language evolution
Zipf's law asserts that word frequency in texts follows a power-law distribution, and is well established empirically, independent of language. We briefly discuss the classical models of Simon and of Mandelbrot, and focus on a recent model by Ferrer i Cancho and Sole' which attempts to explain Zipf's law by a minimum effort principle. The numerical minimization of the effort functional shows a well-definite qualitative change in the structure of the solution when the speaker's and hearer's cost have the same weight. Near this transition word frequency is distributed according to Zipf's law. This situation is reminiscent of the critical behavior of correlated system near phase transitions. We push this analogy as far as we can and show that indeed Ferrer's model may be studied as an ordering phase transition on a suitable skeletal simplex, and the solutions can be found analytically.
Work in progress with Giovanni Zanzotto (U.Padova, Italy) and Ramon Ferrer i Cancho (Universitat Politecnica de Catalunya, Barcelona).
THURSDAY, November 1, 2007