Iterating random functions on a finite set
  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. 
W.M.Y. Goh, P. Hitczenko, E. Schmutz