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.
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