Alice Contat

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20202025

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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

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…