arXiv subjects
Publications and source records attributed to Adrianus Twigt.
We present a simple trimming algorithm that generates nested uniform binary plane trees by removing leaves one-by-one using a best-of-three-match procedure. While its one-step transition specializes to the Luczak-Winkler & Caraceni-Stauffer coupling, its scaling limit provides a suprising c\`adl\`ag erasure of Brownian trees, reminiscent of SLE theory.
Can we obtain a Brownian CRT of mass $1/2$ from a CRT of mass $1$ by cutting certain branches? In this paper, we will answer that question in the much more general setting of self-similar Markov trees. Self-similar Markov trees (ssMt) are random decorated trees that encode the genealogy of a system of particles carrying positive labels, and where particles undergo splitting and growth depending on their labels in a self-similar fashion. Introduced and developed in the recent monograph (Bertoin-Curien-Riera, 2024), they provide a broad generalization of Brownian and stable continuum random trees and arise naturally in various models of random geometry such as the Brownian sphere/disk. The law of a ssMt is characterized by its quadruplet $(\mathrm{a}, \sigma^2, \boldsymbol{\Lambda}; \alpha)$, which specifies the features of the underlying growth-fragmentation mechanism, together with the initial decoration $x>0$. In this work, we focus on special cases of ssMt in which the trees started from different initial values $x>0$ can be coupled into a continuous, increasing family of nested subtrees. In the case of the Brownian and stable continuum random trees, this yields surprisingly simple novel dynamics corresponding to the scaling limit of the leaf-growth algorithms of Luczak-Winkler and Caraceni-Stauffer.