Parking on the Random Recursive Tree
Résumé
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.
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