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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 epsilon > 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 epsilon(c) = 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.
- Lanchier, Nicolas (Author)
- College of Liberal Arts and Sciences (Contributor)
Lanchier, N. (n.d.). The critical value of the Deffuant model equals one half. ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 9(2), 383–402.
- 2014-02-28 03:43:10
- 2021-10-27 11:59:28
- 2 years 10 months ago