Probability laws in multi-dimensional noisy HK-models

Anton Bolychev, Anatoly Manita

Abstract:

The classical Hegselmann-Krause opinion dynamics model is known for the
simplicity of its interaction rules and for the striking complexity of its collective behavior
observed in computer simulations. The nonlinearity of the dynamics makes an analytical study
of the model a very hard task. Recently there is some interest in introducing a random noise in
the HK dynamics. In our study we focus on exact analysis of probability laws for a noisy HK
model and give a detailed description of distribution transformations related to such systems.
Our results shed some light on a long-time behavior of the noisy HK model and open new
possibilities for future analytical and numerical studies in this area.