Local theorems related to Lévy-type branching mechanism
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We prove local limit theorems for the total mass processes of two branchingfluctuating particle systems which converge to discontinuous (2, d, )-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 + (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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it