Generic alignment conjecture for systems of Cucker–Smale type

The generic alignment conjecture states that for almost every initial data on the torus solutions to the Cucker–Smale system with a strictly local communication align to the common mean velocity. In this note, we present a partial resolution of this conjecture using a statistical mechanics approach. First, the conjecture holds in full for the sticky particle model representing, formally, infinitely strong local communication. In the classical case, the conjecture is proved when N , the number of agents, is equal to 2. It follows from a more general result, stating that for a system of any size for almost every data at least two agents align. The analysis is extended to the open space R n in the presence of confinement and potential interaction forces. In particular, it is shown that almost every non-oscillatory pair of solutions aligns and aggregates in the potential well.