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| URL: http://arxiv.org/pdf/physics/0512045 |
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| Authoritative: http://dx.doi.org/10.1103/PhysRevE.73.015102 (Publisher's PDF... likely be available here.) |
| Source: http://arxiv.org/abs/physics/0512045 |
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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 which requires less cognitive effort of the agents, with respect to the mean-field case, but takes longer to complete. In 1-d 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 N^{1+2/d} in dimension d<5 (d=4 being the upper critical dimension), while in mean-field both memory and time scale as N^{3/2}, for a population of N agents. We present analytical and numerical evidences supporting this picture.BibTex
@article{baronchelli05topologyLanguageGame,
author={A. Baronchelli and L. Dall'Asta and A. Barrat and V. Loreto},
title={Topology Induced Coarsening in Language Games},
journal={Physical Review E},
year={2005},
volume={73},
pages={015102},
doi={10.1103/PhysRevE.73.015102},
url={http://www.isrl.uiuc.edu/~amag/langev/paper/baronchelli05topologyLanguageGame.html}
}
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