Alice Contat : How to park a car on a tree ?

par Dr Alice Contat (LAGA, Université Sorbonne Paris Nord)

jeudi 5 mars 2026, 10:30 → 11:30 Europe/Paris

Salle de Séminaire (IDP-Orléans)

We consider a rooted tree whose vertices are interpreted as parking spaces, each of which can accommodate at most one car. Cars arrive at the vertices and attempt to park. Each car first tries to park at its arrival vertex; if it is already occupied, the car moves toward the root until it finds the first available space. If no space is available along this path to the root, the car leaves the tree without parking and contributes to the outgoing flow of cars.

When the number of arriving cars is small, almost all of them manage to find a parking space. However, when arrivals are too numerous, one can expect that a positive proportion of cars will fail to park.

In this talk, I will present several tools to study the phase transition that occurs between these two regimes, depending on the type of trees and arrival processes considered.