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On families of weakly dependent random variables

Tomasz Łuczak (2011)

Banach Center Publications

Let ( k ) be a family of random independent k-element subsets of [n] = 1,2,...,n and let ( ( k ) , ) = ( k ) ( ) denote a family of ℓ-element subsets of [n] such that the event that S belongs to ( k ) ( ) depends only on the edges of ( k ) contained in S. Then, the edges of ( k ) ( ) are ’weakly dependent’, say, the events that two given subsets S and T are in ( k ) ( ) are independent for vast majority of pairs S and T. In the paper we present some results on the structure of weakly dependent families of subsets obtained in this way. We also list...

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