Stochastic block–monotonicity in the approximation of the stationary distribution of infinite markov chains
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Bibliographic record
Abstract
Markov chains with block-structured transition matrices find many applications in various areas. Such Markov chains are characterized by having a state space which is partitioned into levels, each level consisting of a number of stages. Examples include Markov chains of GI/M/1 type and M/G/l type, and, more generally, Markov chains of Toeplitz type. The level-dependent quasi-birth-and-death (LDQBD) process provides an additional example; the transition matrix does not have repeating blocks in this case. In the analysis of such Markov chains, a number of properties and/or measures which relate to transitions among levels play a dominant role, while transitions between stages within the same level are less important In this paper, we introduce the concept of block-monotonicity and apply this notion to the analysis of Markov chains possessing block structure. In particular, the problem of approximating the stationary probability vectors is successfully treated
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| 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