2023/12/07 by Alice Contat, Contat, Alice
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2312.04472
openalex publication_date 2023/12/07 · openalex created_date 2023/12/09 · openalex updated_date 2026/07/28
Consider a rooted tree on the top of which we let cars arrive on its vertices. Each car tries to park on its arriving vertex but if it is already occupied, it drives towards the root of the tree and parks as soon as possible. In this article, we establish a natural coupling between the parking process on trees with prescribed degrees and an oriented configuration model. As a consequence, we recover the location of the phase transition for parking on critical Bienaymé--Galton--Watson trees already proven by Curien and Hénard, and Contat.