Convergence analysis of heterogeneous Deffuant-Weisbuch model

In this paper, we consider the dynamics of heterogeneous Deffuant-Weisbuch (DW) model. Different from homogeneous DW model, the convergence analysis is much complicated because the selected agent's opinion value would not be in the acceptable confidence neighbor of the corresponding agent who selects it unlike the uniform confidence radius case in the homogeneous DW model. For the first time, we prove that the convergence is reached almost surely, and the absolute difference of any two agents' limit opinion values are either zero or larger than the smallest confidence radius almost surely in the trajectory probability space about the heterogeneous DW model.