Iterating random functions on a finite set
Combinatorics
2007-05-23 v2 Probability
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.
Cite
@article{arxiv.math/0207276,
title = {Iterating random functions on a finite set},
author = {W. M. Y. Goh and P. Hitczenko and E. Schmutz},
journal= {arXiv preprint arXiv:math/0207276},
year = {2007}
}
Comments
update references and conjecture's status