Bibliographic record
Abstract
We prove local limit theorems for the total mass processes of two branchingfluctuating particle systems which converge to discontinuous (2, d, β)-superprocess.To this end, we establish new subtle properties of the total mass for this class of superprocesses.Thus, the density of its absolutely continuous component exhibits a polynomial blow-up at the origin and has a regularly varying upper tail.Both particle systems considered are characterized by the same heavy-tailed branching mechanism that belongs to the domain of normal attraction of an extreme stable law with index 1 + β ∈ (1, 2).One of them starts from a Poisson field, whereas the initial number of particles for the other system is non-random.We demonstrate that the poissonization of the initial field of particles is related to Gnedenko's method of accompanying infinitely divisible laws.The comparison of our results with their 'continuous' counterparts (which pertain to convergence to the super-Brownian motion) reveals a worse discrepancy between the extinction probabilities.This is explained through the intrinsic difference between structures of individual surviving clusters.
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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 | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
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".