Sure Event Problem in Multicomponent Dynamical Systems with Attractive Interaction

Abstract

We establish a series of sufficient conditions for the realization of a sure event as the limit (in time) state of a multicomponent dynamical system with attractive interaction. The sure event is characterized by the state of a system with finitely many positions when all coordinates of the distribution are equal to zero, except a single fixed coordinate equal to 1. The sure event can be interpreted as the state of consensus in social networks and, hence, the obtained results can be used in voter and opinion-formation models.