Abstract
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.
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.
| Original language | English |
|---|---|
| Article number | 65 |
| Number of pages | 35 |
| Journal | Journal of Statistical Physics |
| Volume | 192 |
| Early online date | 29 Apr 2025 |
| Publication status | Published - 29 Apr 2025 |