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.

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关于随机变量序列排列的联合典型性

随机变量相关序列的排列自然出现在各种应用中，例如图形匹配和异步通信。在本文中，研究了这种置换序列的渐近统计行为。假设随机向量的集合是基于任意联合分布产生的，并且向量经过置换操作。研究了所得置换向量相对于原始分布的联合典型性。作为初始步骤，考虑相关随机向量对的排列。结果表明，置换向量的联合典型性的概率仅取决于置换的不相交循环的数量和长度。因此，研究一类称为'的排列的典型性就足够了 标准排列'，为此，推导出联合典型性概率的上限。标准置换的概念被扩展到一类称为“贝尔置换向量”的置换向量。通过研究 Bell 置换向量，可以推导出任意随机序列集合的置换的联合典型性概率的上限。