The asymptotic distribution of the diameter of a random mapping (Q1608730)

The authors give an asymptotic distribution of the diameter of the digraph of a uniformly distributed random mapping of an \(n\)-element set to itself as the distribution of a functional of reflecting Brownian bridge. This yields a formula for the Mellin transform of the asymptotic distribution, generalizing the evaluation of its mean by \textit{P. Flajolet} and \textit{A. M. Odlyzko} [in: Advances in cryptology -- EUROCRYPT '89. Lect. Notes Comput. Sci. 434, 329-354 (1990; Zbl 0747.05006)]. The methodology should be applicable to other characteristics of random mappings.