Parking on the Random Recursive Tree
Alice Contat, Lucile Laulin

TL;DR
This paper investigates the parking process on random recursive trees, revealing a phase transition at zero density and identifying the critical window for car flux, especially for binary arrivals, in large trees.
Contribution
It is the first to analyze the parking process on trees with large degree vertices, establishing phase transition behavior and critical thresholds.
Findings
Phase transition occurs at density 0.
Critical window for positive flux identified at density ~ log(n)^{-2+o(1)}.
First study of parking on trees with large degree vertices.
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 . 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 where 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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Taxonomy
TopicsStochastic processes and statistical mechanics · Mathematical Dynamics and Fractals · Data Management and Algorithms
