The steady state cluster

par Eleanor Archer (CEREMADE)

jeudi 15 janv. 2026, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (ICJ)

The steady state cluster was introduced by Edward Crane in 2018 as the conjectured stationary state of the Ráth-Tóth forest fire model and can be defined as the random finite rooted tree C satisfying the following recursive equation: C is a singleton with probability 1/2 and otherwise is obtained by joining by an edge the roots of two independent trees C′ and C′′, each having the law of C, and then re-rooting the resulting tree at a uniform random vertex.
We will discuss some properties of this tree: is it a Galton-Watson tree in disguise? And what is its scaling limit?
Based on joint work in progress with Edward Crane.