The limiting theorems for a random walk of two particles on the lattice ??

Abstract

It is shown that the difference between the probability distributions of the particles positions at time t as t↦∞ for homogeneous and inhomogeneous random walk of two particles on the lattice Z3 has an order \(\left( {\frac{|}{{t^3 + \gamma }} + \frac{1}{{t^3 (|z| + 1)}}} \right)\) (γ>0 is a constant), if the distance |z| between the particles is large enough. As a consequence the integral limit theorem was proved in this case.