Hierarchical Cucker-Smale Model Subject to Random Failure

Consider a system of autonomous interacting agents in R³, where each agent adjusts its velocity according to its own past velocity and a weighted mean of the relative velocities of its superiors in a certain prescribed hierarchy. Furthermore, each agent, at each time step, can fail to see any of its superiors with a certain probability, the failure rate probability. We prove that for agent interactions with linear or sub-linear distance dependent rate of decay, the flocking results valid for the non-failure deterministic model introduced by Shen also hold true, independently of the failure rate probability.