The asymptotic distribution of the diameter of a random mapping
نویسندگان
چکیده
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 re ecting 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). Titre: La loi limite du diam etre d'une application al eatoire. R esum e: On exprime la loi limite du diam etre du digraphe d'une application al eatoire, choisie uniform ement parmi les applications d'un ensemble a n el ements dans lui-même, comme la loi d'une fonctionnelle du pont brownien r e echi. Ceci donne une formule pour la transform ee de Mellin de cette loi limite, g en eralisant la formule pour sa moyenne due a Flajolet et Odlyzko (1990). Research supported in part by N.S.F. Grants DMS-9970901 and DMS-0071448
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