  Using a simple probabilistic model, we illustrate that a small part of a
strongly correlated many-body classical system can show a paradoxical behavior,
namely asymptotic stochastic independence. We consider a triangular array such
that each row is a list of $n$ strongly correlated random variables. The
correlations are preserved even when $n\to\infty$, since the standard central
limit theorem does not hold for this array. We show that, if we choose a fixed
number $m<n$ of random variables of the $n$th row and trace over the other
$n-m$ variables, and then consider $n\to\infty$, the $m$ chosen ones can,
paradoxically, turn out to be independent. However, the scenario can be
different if $m$ increases with $n$. Finally, we suggest a possible
experimental verification of our results near criticality of a second-order
phase transition.
