Bibliographic record
Abstract
We prove an asymptotic Edgeworth expansion for the profiles of certain random\ntrees including binary search trees, random recursive trees and plane-oriented\nrandom trees, as the size of the tree goes to infinity. All these models can be\nseen as special cases of the one-split branching random walk for which we also\nprovide an Edgeworth expansion. These expansions lead to new results on mode,\nwidth and occupation numbers of the trees, settling several open problems\nraised in Devroye and Hwang [Ann. Appl. Probab. 16(2): 886--918, 2006], Fuchs,\nHwang and Neininger [Algorithmica, 46 (3--4): 367--407, 2006], and Drmota and\nHwang [Adv. in Appl. Probab., 37 (2): 321--341, 2005]. The aforementioned\nresults are special cases and corollaries of a general theorem: an Edgeworth\nexpansion for an arbitrary sequence of random or deterministic functions\n$\\mathbb L_n:\\mathbb Z\\to\\mathbb R$ which converges in the mod-$\\phi$-sense.\nApplications to Stirling numbers of the first kind will be given in a separate\npaper.\n
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.005 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".