The Poisson approximation for the number of matches of values of a discrete function from chains

We find conditions which are sufficient for convergence of the distribution of the number of matches of values of a function considered on tuples of arguments taken from a sequence of independent identically distributed random variables to the Poisson law and estimate the convergence rate. We derive a series of corollaries of this result. In particular, in the equiprobable polynomial scheme we obtain Poisson limit theorems for the number of pairs of non-overlapping tuples with identical frequencies of occurrences of symbols and for the number of pairs of tuples with identical structure.
This research was supported by the Program of President of Russian Federation for supporting young Russian scientists, grant 2831.2003.09.