ON A COMBINATORIAL STRONG LAW OF LARGE NUMBERS

Year 2018, Volume: 11 Issue: 3, 46 - 52, 31.12.2018

Andrei N. Frolov

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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