Macroscopic population-level behavior may be observed in large systems of interacting particles. These phenomena are not encoded in the individual particles, but they emerge when the number of particles is large enough. How do these phenomena emerge? Motivated by concrete applications in physics and biology, this question is discussed in the cases of (1) systems of coalescing particles, and (2) dense hard-particle systems.

 

Coalescing particle systems are studied at the mesoscopic scale using Smoluchowski coagulation-type equations. Longtime behavior and emergence of patterns in multicomponent systems are obtained by means of fixed-point arguments and measure theorical tools.