Topology Induced Coarsening in Language Games
<|reference_start|>Topology Induced Coarsening in Language Games: 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.<|reference_end|>
@article{baronchelli2005topology,
    title={Topology Induced Coarsening in Language Games},
    author={A. Baronchelli, L. Dall'Asta, A. Barrat, V. Loreto},
    journal={Phys. Rev. E 73, 015102(R) (2006)},
    year={2005},
    doi={10.1103/PhysRevE.73.015102},
    archivePrefix={arXiv},
    eprint={physics/0512045},
    primaryClass={physics.soc-ph cond-mat.stat-mech cs.GT cs.MA}
}