ELFT HÍRADÓ

[Geza Odor <odor.geza AT ttk.mta.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 λ, as 
obtained previously via other methods [2-4]. (λ 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 λ-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


---------------------
www.mfa.kfki.hu/~odor