We investigate the two-word Naming Game on two-dimensional random geometricgraphs. Studying this model advances our understanding of the spatialdistribution and propagation of opinions in social dynamics. A main feature ofthis model is the spontaneous emergence of spatial structures called opiniondomains which are geographic regions with clear boundaries within which allindividuals share the same opinion. We provide the mean-field equation for theunderlying dynamics and discuss several properties of the equation such as thestationary solutions and two-time-scale separation. For the evolution of theopinion domains we find that the opinion domain boundary propagates at a speedproportional to its curvature. Finally we investigate the impact of committedagents on opinion domains and find the scaling of consensus time.
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