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Topology-induced coarsening in language games

Andrea Baronchelli, Luca Dall’Asta, Alain Barrat, and Vittorio Loreto
Phys. Rev. E 73, 015102(R) – Published 18 January 2006

Abstract

We investigate how very large populations are able to reach a global consensus, out of local “microscopic” interaction rules, in the framework of a recently introduced class of models of semiotic dynamics, the so-called naming game. We compare in particular the convergence mechanism for interacting agents embedded in a low-dimensional lattice with respect to the mean-field case. We highlight that in low dimensions consensus is reached through a coarsening process that requires less cognitive effort of the agents, with respect to the mean-field case, but takes longer to complete. In one dimension, the dynamics of the boundaries is mapped onto a truncated Markov process from which we analytically computed the diffusion coefficient. More generally we show that the convergence process requires a memory per agent scaling as N and lasts a time N1+2d in dimension d4 (the upper critical dimension), while in mean field both memory and time scale as N32, for a population of N agents. We present analytical and numerical evidence supporting this picture.

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  • Received 23 September 2005

DOI:https://doi.org/10.1103/PhysRevE.73.015102

©2006 American Physical Society

Authors & Affiliations

Andrea Baronchelli1, Luca Dall’Asta2, Alain Barrat2, and Vittorio Loreto1

  • 1Dipartimento di Fisica, Università “La Sapienza” and SMC-INFM, Piazzale Aldo Moro 2, 00185 Rome, Italy
  • 2Laboratoire de Physique Théorique, UMR du CNRS 8627, Bâtiment 210, Université de Paris-Sud, 91405 Orsay Cedex, France

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Vol. 73, Iss. 1 — January 2006

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