Dynamic monopolies with randomized starting configuration

Properties of systems with majority voting rules have been extensively studied. In this work we focus on the randomized case, where the system is initialized by random initial set of seeds. Our main aim is to find an asymptotic estimate for sampling probability, so that the initial set of seeds is (not) almost surely a dynamic monopoly. After presenting some trivial examples, we present extensive results for toroidal mesh and random 4-regular graph under simple majority scenario.