I am trying to find a characterization of the probability that vertex $1$ is connected to an arbitrary large vertex $N$ in a random digraph.
The difference from typical random digraphs is that if $(i,j)$ is an edge then $i < j$, i.e., edges can only go from lower indexed vertex to higher indexed vertex.
Is there a term for this type of digraph? And is there any references anyone can suggest?
Thank you very much for any help you can offer.