A random intersection digraph: Indegree and outdegree distributions

Let S(1),…,S(n),T(1),…,T(n)S(1),…,S(n),T(1),…,T(n) be random subsets of the set [m]={1,…,m}[m]={1,…,m}. We consider the random digraph DD on the vertex set [n][n] defined as follows: the arc i→ji→j is present in DD whenever S(i)∩T(j)≠0̸S(i)∩T(j)≠0̸. Assuming that the pairs of sets (S(i),T(i))(S(i),T(i)), 1≤i≤n1≤i≤n, are independent and identically distributed, we study the in- and outdegree distributions of a typical vertex of DD as n,m→∞n,m→∞.