The asymptotic distribution of the diameter of a random mapping

February, 2002
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).

PDF File: 
Postscript File: