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Brownian bridge asymptotics for random mappings. (English) Zbl 0811.60057
This paper deals with the uniform model of random mappings of an $$n$$- element set into itself. The authors introduce a new technique, which starts by specifying a coding of mappings as walks with $$\pm 1$$ steps. Then, the uniform random mapping model is thereby coded as a nonuniform random walk. The main result of the paper shows that as $$n\to\infty$$ the random walk rescales to reflecting Brownian bridge. This enables to obtain a large number of limiting distributions concerning numerical characteristics of the random digraphs representing random mappings.

##### MSC:
 60G50 Sums of independent random variables; random walks 60J65 Brownian motion 60C05 Combinatorial probability 60F05 Central limit and other weak theorems 05C80 Random graphs (graph-theoretic aspects)
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