Modified log-Sobolev inequalities for strong-Rayleigh measures
Bibliographic record
Abstract
We establish universal modified log-Sobolev inequalities for reversible Markov chains on the boolean lattice {0,1}n, when the invariant law π satisfies a form of negative dependence known as the stochastic covering property. This condition is strictly weaker than the strong Rayleigh property, and is satisfied in particular by all determinantal measures, as well as the uniform distribution over the set of bases of any balanced matroid. In the special case where π is k-homogeneous, our results imply the celebrated concentration inequality for Lipschitz functions due to Pemantle and Peres (Combin. Probab. Comput. 23 (2014) 140–160). As another application, we deduce that the natural Monte-Carlo Markov chain used to sample from π has mixing time at most knloglog1π(x) when initialized in state x. To the best of our knowledge, this is the first work relating negative dependence and modified log-Sobolev inequalities.
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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 | 0.004 | 0.026 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 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".