MERCREDI 8 AVRIL 2009 14 heures Salle Séminaire 5 Centre de Physique Théorique Marseille-Luminy Timoteo Carletti Department of Mathematics FUNDP, Namur, Belgique Title: Opinion dynamics: friendship and social temperature Abstract: We propose a model of opinion dynamics model where agents adjust their current opinion as a result of random encounters, allowing to study the mechanism of group formation under the pressure of two antagonist forces: friendship and social temperature. Every agent is characterized by a scalar continuous opinion about a given subject and his friendship relations with other agents (roughly speaking a measures of the mutual trust). The important fact is that both quantities evolve in time in a non trivial way. As a result of the interactions, clusters of individuals sharing the same opinion and displaying high affinity-friendship values are formed. The distribution of the clusters is monitored and a second order phase transition detected, marking the distinction between a full connected group and a fragmented population. The control parameter is represented by an effective radius that specifies the range of the interaction between agents. The system relaxation time is also computed and a close analytical estimate derived. Our results can be restated as a opinion model developing on a social network where the network itself is not a static one but it evolves, being the affinity-friendship matrix strictly related to the adjacency matrix. Moreover we are able to analytically describe the network evolution in terms of its topological parameters (i.e. mean degree, clustering coefficient, mean path, diameter).