  Permutations of correlated sequences of random variables appear naturally in
a variety of applications such as graph matching and asynchronous
communications. In this paper, the asymptotic statistical behavior of such
permuted sequences is studied. It is assumed that a collection of random
vectors is produced based on an arbitrary joint distribution, and the vectors
undergo a permutation operation. The joint typicality of the resulting permuted
vectors with respect to the original distribution is investigated. As an
initial step, permutations of pairs of correlated random vectors are
considered. It is shown that the probability of joint typicality of the
permuted vectors depends only on the number and length of the disjoint cycles
of the permutation. Consequently, it suffices to study typicality for a class
of permutations called 'standard permutations', for which, upper-bounds on the
probability of joint typicality are derived. The notion of standard
permutations is extended to a class of permutation vectors called 'Bell
permutation vectors'. By investigating Bell permutation vectors, upper-bounds
on the probability of joint typicality of permutations of arbitrary collections
of random sequences are derived.
