Predecessors in a random mapping

Ž . 4 ABSTRACT: A random mapping T ; q of a finite set V, Vs 1, 2, . . . , n into itself assigns independently to each igV its unique image jgV with probability q if is j and with Ž . Ž . probability Ps 1yq r ny1 if i/ j. The number of predecessors of elements from a given subset of V is studied. Exact results and limit theorems for the distribution of this random variable, the quasi-binomial distribution, are given. The results are applied to an Ž . inverse epidemic process on a random digraph G representing T ; q . Q 1998 John Wiley & T Sons, Inc. Random Struct. Alg., 13, 501]519, 1998