期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2012
卷号：IX
期号：2
页码：383-402
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：Similarly to the popular voter model, the Deffuant model describesopinion dynamics taking place in spatially structured environments represented bya connected graph. Pairs of adjacent vertices interact at a constant rate. If theopinion distance between the interacting vertices is larger than some confidencethreshold > 0, then nothing happens, otherwise, the vertices’ opinions get closerto each other. It has been conjectured based on numerical simulations that thisprocess exhibits a phase transition at the critical value c = 1/2. For confidencethresholds larger than one half, the process converges to a global consensus, whereascoexistence occurs for confidence thresholds smaller than one half. In this article,we develop new geometrical techniques to prove this conjecture.
关键词：Interacting particle system; random walks; social dynamics
