@article{Baronchelli_PhysRevE_2006, author = {Andrea Baronchelli and Luca Dall'Asta and Alain Barrat and Vittorio Loreto},journal = {PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS},note = {language},pages = {015102--015105},publisher = {AMERICAN PHYSICAL SOC, ONE PHYSICS ELLIPSE, COLLEGE PK, USA, MD, 20740-3844},title = {Topology induced coarsening in language games},type = {article},volume = {73},year = {2006},url = {https://link.aps.org/doi/10.1103/PhysRevE.73.015102},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 N^(1+2/d) in dimension d <=4 (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 evidence supporting this picture.}}