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[Fizinfo] Prof. Ronald Dickman eloadasa

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  • From: Geza Odor <odor.geza AT>
  • To: fizinfo AT
  • Subject: [Fizinfo] Prof. Ronald Dickman eloadasa
  • Date: Mon, 5 Aug 2013 13:48:11 +0200 (CEST)
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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

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


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