### Abstract

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 ε_{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.

Original language | English (US) |
---|---|

Pages (from-to) | 383-402 |

Number of pages | 20 |

Journal | Alea |

Volume | 9 |

Issue number | 2 |

State | Published - 2012 |

### Fingerprint

### Keywords

- Interacting particle system
- Random walks
- Social dynamics.

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

**The critical value of the deffuant model equals one half.** / Lanchier, Nicolas.

Research output: Contribution to journal › Article

*Alea*, vol. 9, no. 2, pp. 383-402.

}

TY - JOUR

T1 - The critical value of the deffuant model equals one half

AU - Lanchier, Nicolas

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Interacting particle system

KW - Random walks

KW - Social dynamics.

UR - http://www.scopus.com/inward/record.url?scp=84877015888&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84877015888&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84877015888

VL - 9

SP - 383

EP - 402

JO - Alea

JF - Alea

SN - 1980-0436

IS - 2

ER -