arXiv:1401.0115v1 [math.DS] 31 Dec 2013 Spatial propagation of opinion dynamics: Naming Game on Random Geographic Graph Weituo Zhang, Chjan Lim, G. Korniss and B. K. Szymanski April 13, 2019 Abstract An agent-based model, Naming Game, on 2-dimensional random geographic networks is investigated. Naming Game, arising from the linguistic study, is one type of opinion dynamics which captures the large scale agreement by pair-wise communications. Study of this model helps to understand the spatial distribution and propagation of social opinions. A main feature of this model is the automatic emer- gence of opinion domains which are clusters sharing the same opinion with clear geographic boundaries. We propose a geographic coarsen- ing approach to analyze this model and obtain a PDE for macrostate dynamics. We discuss several properties of the equation such as the stationary solutions and adiabaticity, and find the evolution of opin- ion domains is qualitatively the same as the Glauber ordering at zero temperature. Finally we consider the effect of committed agents on opinion domains and find the scaling of consensus time. 1 Introduction Opinion dynamics driven by local communication on geographically embed- ded network is of great interest to understand the spatial distribution and propagation of social opinions. Naming Game on random geographic graph investigated in this paper serves as a minimum model of this type. Nam- ing game, originally arise from linguistic studies [1, 2], is proposed to show how agents can achieve global agreement through pair-wise communication without a coordinator. Behavior of Naming Game on various networks have been studied [19, 4, 5, 6, 14, 15]. Random geographic graph(RGG), also referred to as spatial Poisson or Boolean graphs, is a random graph model 1