French Japanese Conference on Probability & Interactions

Where Do Random Trees Grow Leaves

8 mars 2024, 14:20

50m

Centre de conférences Marilyn et James Simons (Le Bois-Marie)

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 $(T_n:n\ge 1)$ 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.

Documents de présentation

Nicolas Curien.pdf

Vidéo