Critical Self-Similar Markov Trees

Nicolas Curien; Xingjian Hu; Dongjian Qian

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arXiv · 2603.16408

Critical Self-Similar Markov Trees

Nicolas Curien·Xingjian Hu·Dongjian Qian

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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.

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Nicolas Curien, Xingjian Hu, Dongjian Qian. 2026-03-17. Critical Self-Similar Markov Trees. https://arxiv.org/abs/2603.16408

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