Asymptotics in Random Recursive Circuits*

The number of descendants in a random directed acyclic graph

“…7.2.2.3–371 in [13]). Among results shown earlier for random $$$ d $$$‐dags, we mention results on vertex degrees and leaves [9, 14–16, 18], and on lengths of paths and depth [1, 6, 8, 10, 19].…”

“…Moment convergence then follows from the bounds (8. 16) and (8.17) as in the case 𝑑 = 2. Finally, the moment convergence and (1.8) yield (1.6).…”

“…The random $$$ d $$$‐dag has been studied as a model for a random circuit where each gate has $$$ d $$$ inputs chosen at random [1, 6, 10, 16, 18, 19]. (In this case it seems more natural to reverse all edges, and regard a $$$ d $$$‐dag as a graph with indegrees 0 or $$$ d $$$.…”