ELFT HÍRADÓ

[Geza Odor <odor AT mfa.kfki.hu>]

SZFI Kollokvium

Ronald Dickman

Federal University of Minas Gerais, Brasil
Analysis of an information-theoretic model for communication

We examine the cost-minimization problem posed by Ferrer i Cancho and Solé
in their information-theory based communication model [1], proposed in
efforts to explain Zipf's Law (that is, a power-law frequency-rank 
relation
for words in written texts). Using a simple inequality, we obtain the 
exact
minimum-cost solution as a function of the param- eter ?, as obtained
previously via other methods [2-4]. (? defines the relative weights of
speaker's and listener's costs.) We show that at the phase transition, the
minimum-cost solutions do not correspond to a power law except for a
vanishingly small subset, even if we impose the additional condition of
equal costs to speaker and listener [5]. Finally we consider the model at
finite temperature using mean-field theory and entropic Monte Carlo
simulation, and find a line of discontinuous phase transitions in the ?-T
plane. The simulations yield no evidence for a power-law frequency-rank
distribution.

1. R. Ferrer i Cancho and R. V. Solé, PNAS 100, 788 (2003).
2. R. Ferrer i Cancho and A. Díaz-Guilera, J. Stat. Mech.: Theory Exp.
(2007) P06009. 3. A. Trosso, Master's thesis, 2008, University of Turin,
Italy.
4. M. Prokopenko, N. Ay, O. Obst, and D. Polani, J. Stat. Mech. (2010)
P11025.
5. R. Dickman, N. R. Moloney, and E. G. Altmann, J. Stat. Mech. 2012, 
P12022
(2012).

2013. augusztus 13, kedd, 10:00:00
I. épület, Tanácsterem


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