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The asymptotic distribution of the diameter of a random mapping. (English) Zbl 1002.60075

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 P. Flajolet and 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.

MSC:

60J65 Brownian motion

Citations:

Zbl 0747.05006
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References:

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