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<p>In this paper, we study the precise deviations for the number of branches of a random binary tree in the context of Horton–Strahler analysis. We establish precise large deviations, precise moderate deviations, and Cramér-type moderate deviations for the number of branches of the random binary tree. As a consequence of the Cramér-type moderate deviations, a Berry–Esseen bound is derived. The derivations of these results rely heavily on asymptotic analysis of certain discrete summations.</p>

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Precise Deviations for Branches of the Random Binary Tree in the Horton–Strahler Analysis

  • 期刊论文

  • 发表日期：

    2025年4月29日

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  • Fuqing Gao,
  • Zhi Qu,
  • Youzhou Zhou

摘要

In this paper, we study the precise deviations for the number of branches of a random binary tree in the context of Horton–Strahler analysis. We establish precise large deviations, precise moderate deviations, and Cramér-type moderate deviations for the number of branches of the random binary tree. As a consequence of the Cramér-type moderate deviations, a Berry–Esseen bound is derived. The derivations of these results rely heavily on asymptotic analysis of certain discrete summations.