On a random recursive tree with n vertices, parking is supercritical at every positive density, and the first outward flux for binary car arrivals appears when the mean number of cars per vertex is about (log n)^{-2+o(1)}.
C ONTAT, Sharpness of the phase transition for parking on random trees , Random Structures & Algorithms, 61 (2022), pp
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Parking on the Random Recursive Tree
On a random recursive tree with n vertices, parking is supercritical at every positive density, and the first outward flux for binary car arrivals appears when the mean number of cars per vertex is about (log n)^{-2+o(1)}.