On the asymptotic properties of the distribution of the number of pairs of $H$-connected chains

The main result of this paper is a theorem about convergence of the distribution of the number of pairs of $H$-connected $s$-tuples in two independent sequences of independent identically distributed variables. The concept of $H$-connection is a generalisation of the concept of $H$-equivalence of tuples. We give sufficient conditions for convergence and an explicit estimate of the rate of convergence. We use the local variant of the Chen–Stein method for estimating the accuracy of Poisson approximation for distribution of the set of dependent random indicators. The main results of this paper were announced in [7].
The research was supported by the Russian Foundation for Basic Research, grants 02–01–00266 and 00–15–96136.