Critical Self-Similar Markov Trees
Probability
2026-03-18 v1
Abstract
Recently introduced and studied in arXiv:2407.07888, a self-similar Markov tree (ssMt) is a random decorated tree that vastly generalises the fragmentation tree. We study here the critical case that was left aside in arXiv:2407.07888. Borrowing techniques from branching random walk, in particular the recent result of A\"id\'ekon--Hu--Shi arXiv:2409.01048, we can complete the picture by constructing critical ssMt, computing their fractal dimension and studying their associated harmonic and length measures using spinal decomposition.
Keywords
Cite
@article{arxiv.2603.16408,
title = {Critical Self-Similar Markov Trees},
author = {Nicolas Curien and Xingjian Hu and Dongjian Qian},
journal= {arXiv preprint arXiv:2603.16408},
year = {2026}
}