3 papers
math.CO2022
Last Car Decomposition of Planar Maps
Alice Contat
We give new equations which characterize the generating functions of planar quadrangulations and planar triangulations, with zero, one or two boundaries. The proof is inspired by t…
math.PR2021
Parking on Cayley trees & Frozen Erdös-Rényi
Alice Contat, Nicolas Curien
Consider a uniform rooted Cayley tree with vertices and let cars arrive sequentially, independently, and uniformly on its vertices. Each car tries to park on its ar…
math.PR2020
Sharpness of the phase transition for parking on random trees
Alice Contat
Recently, a phase transition phenomenon has been established for parking on random trees. We extend the results of Curien and Hénard on general Galton--Watson trees and allow diffe…