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Iterating random functions on a finite set

W. M. Y. Goh·P. Hitczenko·E. Schmutz
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Abstract

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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W. M. Y. Goh, P. Hitczenko, E. Schmutz. 2002-10-31. Iterating random functions on a finite set. https://arxiv.org/abs/math/0207276

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