## 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

### Keywords:

uniformly distributed random mapping; Brownian bridge

Zbl 0747.05006
Full Text:

### References:

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