We describe, at the microscopic level, the dynamics of N interactingView original: http://arxiv.org/abs/1202.5251
components where the probability is very small when N is large that a given
component interact more than once, directly or indirectly, up to time t, with
any other component. Due to this fact, we can consider, at the macroscopic
level, the quadratic system of differential equations associated with the
interaction and establish an explicit formula for the solution of this system.
We moreover apply our results to some models of Econophysics.