Systems of many interacting particles described by coupled ODEs with random initial conditions appear in many problems of physics, chemistry, biology, social science, and economics. Many important phenomena in such systems is characterized by two-particle correlation function. Direct computation of this function may be prohibitively expensive if the number of particles is large and randomness requires many realizations of their initial locations. In this talk I will present a deterministic approach of finding the two-particle correlation function, based on an appropriate truncation of the BBGKY hierarchy. The derivation of such a truncation will be presented, and comparison with classical truncations such as Kirkwood Superposition Approximation will be provided. It will also be shown that key properties of two-particle correlation function are preserved by this truncation, and numerical comparison with results of Monte Carlo simulations for the original coupled ODE system will be presented.

This is a joint work with L. Berlyand (PSU), R. Creese (PSU), and P.-E. Jabin (U. of Maryland)