We study the parking process on the random recursive tree. We first prove that although the random recursive tree has a non-degenerate Benjamini--Schramm limit, the phase transition for the parking process appears at density $0$. We then identify the critical window for appearance of a positive flux of cars with high probability. In the case of binary car arrivals, this happens at density $ \log (n)^{ -2+o(1)}$ where $n$ is the size of the tree. This is the first work that studies the parking process on trees with possibly large degree vertices.
Categories: math.PR math.CO