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The asymptotic distribution of the diameter of a random mapping


The asymptotic distribution of the diameter of the digraph of a uniformly distributed random mapping of an n-element set to itself is represented as the distribution of a functional of a reflecting Brownian bridge. This yields a formula for the Mellin transform of the asymptotic distribution, generalizing the evaluation of its mean by Flajolet and Odlyzko (1990). The methodology should be applicable to other characteristics of random mappings. © 2002 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.

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