Abstract:
In this talk I explore the consequences that individual's desire to be with people sharing some characteristic
(which we refer to as influence) and attraction to good locations has on segregation by
introducing a particle-interaction model where the interaction between individuals
is governed by the two effects mentioned. Since the time evolution of the particle-interaction model
is governed by a large system of ordinary differential equations I will derive a family of local and non-local partial differential equations
which govern the density of the population for each influence level in order to make any analysis tractable.
For the remaining of the talk I will discuss a simplified case where there are two
groups of individuals: one highly influential and one with no influence. The system of PDEs in this
case is reminiscent of a chemotaxis model with two densities which are simultaneously advected by a given velocity field
and repulsed by each other. By analyzing this system I will show that the desire to be situated in a good location enhances segregation.
In fact, I will prove the existence of a unique ground state that shows that segregates the two populations. |