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The probable behavior of an instance of size n of the stable marriage problem, chosen uniformly at random, is studied. The expected number of stable matchings is shown to be asymptotic to e^ - 1 n n for n. The total rank of women by men in the male optimal (pessimal) matching is proved to be close to n In n (respectively, n² / n, with high probability.
Boris Pittel (Wed,) studied this question.