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In Pittel (1989)'s solution to a problem of Knuth (1976) on the expected number of stable matchings between $n$ men and $n$ women under uniform random preferences, it was shown that, as $n \to \infty$,...

In order to successfully apply the Lovasz local lemma, one needs the events to be relatively independent. This (sometimes) works well in the $G(n,p)$ model of random graphs, where the presence or ...