Robustness of Cucker-Smale flocking model
  Consider a system of autonomous interacting agents moving in space, adjusting each own velocity as a weighted mean of the relative velocities of the other agents. In order to test the robustness of the model, we assume that each pair of agents, at each time step, can fail to connect with certain probability, the failure rate. This is a modification of the (deterministic) Flocking model introduced by Cucker and Smale in Emergent behavior in flocks, IEEE Trans. on Autom. Control, 2007, 52 (May) pp. 852-862. We prove that, if this random failures are independent in time and space, and have linear or sub-linear distance dependent rate of decay, the characteristic behavior of flocking exhibited by the original deterministic model, also holds true under random failures, for all failure rates. 
Eduardo Canale, Federico Dalmao, Ernesto Mordecki and Max Souza
math.PR