Large-Time Behavior of Finite-State Mean-Field Systems With Multiclasses
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Bibliographic record
Abstract
We study in this paper large-time asymptotics of the empirical vector associated with a family of finite-state mean-field systems with multiclasses. The empirical vector is composed of local empirical measures characterizing the different classes within the system. As the number of particles in the system goes to infinity, the empirical vector process converges toward the solution to a McKean-Vlasov system. First, we investigate the large deviations principles of the invariant distribution from the limiting McKean-Vlasov system. Then, we examine the metastable phenomena arising at a large scale and large time. Finally, we estimate the rate of convergence of the empirical vector process to its invariant measure. Given the local homogeneity in the system, our results are established in a product space. Funding: This research was supported by Discovery Grant of the Natural Sciences and Engineering Research Council of Canada [NSERC 315660] and by Carleton University.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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