6–8 mars 2024
Le Bois-Marie
Fuseau horaire Europe/Paris

Where Do Random Trees Grow Leaves

8 mars 2024, 14:20
50m
Centre de conférences Marilyn et James Simons (Le Bois-Marie)

Centre de conférences Marilyn et James Simons

Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette

Orateur

Prof. Nicolas Curien (Université Paris-Saclay)

Description

Luczak and Winkler (refined by Caraceni and Stauffer) showed that is it possible to create a chain of random binary trees $(T_n : n \geq 1)$ so that $T_{n}$ is uniformly distributed over the set of all binary trees with $n$ leaves and such that $T_{n+1}$ is obtained from $T_{n}$ by adding "on leaf". We show that the location where this leaf must be added is far from being uniformly distributed on $T_n$ but is concentrated on a "fractal" subset of $n^{3(2- \sqrt{3})+o(1)}$ leaves. The full multifractal spectrum of the measure in the continuous setting is computed. Joint work with Alessandra Caraceni and Robin Stephenson.

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