Alice Contat

activity

20202025

most citedSurprising identities for the greedy independent set on Cayley trees

1 citations · 1 across the 13 of their papers we have counts for

collaborators

14 papers

math.PR2025

Random burning of the Euclidean torus

Guillaume Blanc, Alice Contat

The burning number of a graph is the minimal number of steps that are needed to burn all of its vertices, with the following burning procedure: at each step, one can choose a point…

math.PR2025

Universality for catalytic equations and fully parked trees

Alice Contat, Nicolas Curien

We show that critical parking trees conditioned to be fully parked converge in the scaling limits towards the Brownian growth-fragmentation tree, a self-similar Markov tree differe…

math.CA2025

Blow-up rate of solution to generalised Blasius equation

Guillaume Blanc, Alice Contat

We identify the blow-up rate of a solution to a generalised Blasius equation, that we came across while studying a probabilistic model of "Poissonian burning" in Euclidean space. O…

math.PR2025

Parking on the Random Recursive Tree

Alice Contat, Lucile Laulin

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 transitio…

math.PR2024

The critical Karp--Sipser core of Erdős--Rényi random graphs

Thomas Budzinski, Alice Contat

The Karp--Sipser algorithm consists in removing recursively the leaves as well their unique neighbours and all isolated vertices of a given graph. The remaining graph obtained when…

math.PR2024

Parking on supercritical geometric Bienaymé--Galton--Watson trees

Linxiao Chen, Alice Contat

Consider a supercritical Bienaymé--Galton--Watson tree $T$ with geometric offspring distribution. Each vertex of this tree represents a parking spot which can accommodat…

math.PR2023

Parking on trees with a (random) given degree sequence and the Frozen configuration model

Alice Contat

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 ro…

math.PR2023

Eve, Adam and the Preferential Attachment Tree

Alice Contat, Nicolas Curien, Perrine Lacroix +2

We consider the problem of finding the initial vertex (Adam) in a Barabási--Albert tree process $(T (n) : n \geq 1)$ at large times. More precisely, given $ε > 0$ …

math.PR2022

The critical Karp--Sipser core of random graphs

Thomas Budzinski, Alice Contat, Nicolas Curien

We study the Karp--Sipser core of a random graph made of a configuration model with vertices of degree $1, 2$ and $3$ . This core is obtained by recursively removing the leaves as we…

math.PR2022

Parking on the infinite binary tree

David Aldous, Alice Contat, Nicolas Curien +1

Let $(A_{u} : u \in B)$ be i.i.d.~non-negative integers that we interpret as car arrivals on the vertices of the full binary tree $B$ . Each car tries to park on it…

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 $T_{n}$ with $n$ vertices and let $m$ cars arrive sequentially, independently, and uniformly on its vertices. Each car tries to park on its ar…

math.PR2021★ 1 cited

Surprising identities for the greedy independent set on Cayley trees

Alice Contat

We prove a surprising symmetry between the law of the size $G_{n}$ of the greedy independent set on a uniform Cayley tree $T_{n}$ of size $n$ and that of its complement. We…

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…