Preprints, Working Papers, ... Year : 2025

Parking on the Random Recursive Tree

Abstract

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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Dates and versions

hal-04893363 , version 1 (17-01-2025)

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Alice Contat, Lucile Laulin. Parking on the Random Recursive Tree. 2025. ⟨hal-04893363⟩
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