ON A COMBINATORIAL STRONG LAW OF LARGE NUMBERS

Abstract

We derive strong laws of large numbers for combinatorial sums  iXniπn(i), where Xnij are n × n matrices of random variables with finite fourth moments and (πn(1), . . . , πn(n)) are uniformly distributed random permutations of 1, . . . , n independent with X’s. We do not assume the independence of X’s, but this case is included as well. Examples are discussed.

Keywords

• Combinatorial central limit theorem,combinatorial sums,strong law of large numbers

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