Asymptotics of disordering in the discrete approximation of an Arratia flow

We propose an approach to study the geometrical properties of stochastic flows with coalescence. We consider the discrete time approximation of a stochastic flow. In contrast to flows with continuous time, the ordering of particles in the discrete-time flows does not hold. The disordering in the approximation scheme can be considered as geometrical properties of a stochastic flow. We establish the rate of decrease to zero of the time which two particles spend in the opposite order.