Iterating random functions on a finite set

E. Schmutz; P. Hitczenko; W.M.Y. Goh

Iterating random functions on a finite set

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arxiv math/0207276 v2 pith:4XB5S6FQ submitted 2002-07-29 math.CO math.PR

W.M.Y. Goh , P. Hitczenko , E. Schmutz This is my paper · ORCID

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keywords functionscardinalitychosencompositionconstantdistributionfindfinite

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Let f_1,f_2,..., be functions chosen independently and uniformly from the set of all functions from a set of cardinality n into itself. Let g_t be the composition of the first t functions, and let T be the smallest t for which g_t is constant. We find the limiting distribution of T/n, as n --> infinity.

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