Diffusion with interactions and collisions between coloured particles and the propagation of chaos (Q1072267)

We consider a system of N particles on the real line which are of two different types (colours). Their dynamics is given by a stochastic differential equation with constant diffusion part; the drift felt by a particle of either type depends on the empirical measures of type 1 and 2 particles at every instant; further a reflection condition is imposed so that particles of different type are not allowed to cross each other. The article studies the Vlasov-McKean limit of the system as \(N\to \infty:\) propagation of chaos and an evolution equation for the limiting empirical measures is established, from where in particular an equation for the separating front between the two types follows.