Where Do Random Trees Grow Leaves - A Study of Binary Tree Growth Dynamics

Explore the fascinating world of random binary trees in this 52-minute lecture by Nicolas Curien from Université Paris-Saclay at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the intriguing chain of random binary trees $(T_n : n \geq 1)$ and discover how $T_{n+1}$ is derived from $T_n$ by adding a single leaf. Uncover the surprising concentration of leaf addition on a fractal subset of $n^{3(2- \sqrt{3})+o(1)}$ leaves, challenging the notion of uniform distribution. Learn about the full multifractal spectrum of the measure in the continuous setting, based on joint work with Alessandra Caraceni and Robin Stephenson. Follow along as Curien presents the First Dynamic Binary Tree Algorithm, rational expressions, examples, theorems, simulations, and interpretations, concluding with a comprehensive proof of the findings.