The asymptotic distribution of the diameter of a random mapping

The asymptotic distribution of the diameter of a random mapping

Report Number
606
Authors
David Aldous and Jim Pitman
Citation
PDf
Abstract

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).

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