A random intersection digraph: Indegree and outdegree distributions

Let S(1),…,S(n),T(1),…,T(n) be random subsets of the set [m]={1,…,m}. We consider the random digraph D on the vertex set [n] defined as follows: the arc i→j is present in D whenever S(i)∩T(j)≠0?. Assuming that the pairs of sets (S(i),T(i)), 1≤i≤n, are independent and identically distributed, we study the in- and outdegree distributions of a typical vertex of D as n,m→∞.