Iterating random functions on a finite set
W. M. Y. Goh, P. Hitczenko, E. Schmutz
Abstract
Let f1,f2,..., be functions chosen independently and uniformly from the set of all functions from a set of cardinality n into itself. Let gt be the composition of the first t functions, and let T be the smallest t for which gt is constant. We find the limiting distribution of T/n, as n --> infinity.
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