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 Z 3 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.
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partially supported by Russian Fund of Fundamental Research 93-011-1470.
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Minlos, R.A., Zhizhina, E.A. The limiting theorems for a random walk of two particles on the lattice ℤν . Potential Analysis 5, 139–172 (1996). https://doi.org/10.1007/BF00396776
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DOI: https://doi.org/10.1007/BF00396776