The critical value of the deffuant model equals one half

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24 Scopus citations


Similarly to the popular voter model, the Deffuant model describes opinion dynamics taking place in spatially structured environments represented by a connected graph. Pairs of adjacent vertices interact at a constant rate. If the opinion distance between the interacting vertices is larger than some confidence threshold ε > 0, then nothing happens, otherwise, the vertices' opinions get closer to each other. It has been conjectured based on numerical simulations that this process exhibits a phase transition at the critical value εc = 1/2. For confidence thresholds larger than one half, the process converges to a global consensus, whereas coexistence occurs for confidence thresholds smaller than one half. In this article, we develop new geometrical techniques to prove this conjecture.

Original languageEnglish (US)
Pages (from-to)383-402
Number of pages20
Issue number2
StatePublished - 2012


  • Interacting particle system
  • Random walks
  • Social dynamics.

ASJC Scopus subject areas

  • Statistics and Probability


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