Disordering asymptotics in the discrete approximation of an Arratia flow

E. V. Glinyanaya
Theory of Stochastic Processes
Vol.18 (34), no.2, 2012, pp.8-14
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.