Exponential ergodicity of branching processes with immigration and competition
Bibliographic record
Abstract
Nous étudions la propriété ergodique d’un processus de branchement en temps et espace continu avec immigration et compétition. L’ergodicité exponentielle dans une distance de variation totale pondérée est prouvée sous des hypothèses naturelles. Le théorème principal s’applique aux mécanismes de branchement sous-critiques, critiques et sur-critiques, y compris tous les types stables. La démonstration est basée sur la construction d’un processus Markovien de couplage et le choix d’une fonction de contrôle non symétrique pour la distance. Ces éléments sont conçus pour identifier et profiter du facteur dominant des mécanismes de branchement, d’immigration et de compétition dans différentes parties de l’espace d’états. Cette approche permet de trouver une borne inférieure pour le taux d’ergodicité.
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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 | 0.007 | 0.031 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.005 | 0.006 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".