Bibliographic record
Abstract
Many integrable stochastic particle systems in one space dimension (such as TASEP -totally asymmetric simple exclusion process -and its various deformations, with a notable exception of ASEP) remain integrable when we equip each particle x i with its own jump rate parameter ν i .It is a consequence of integrability that the distribution of each particle x n (t) in a system started from the step initial configuration depends on the parameters ν j , j ≤ n, in a symmetric way.A transposition ν n ↔ ν n+1 of the parameters thus affects only the distribution of x n (t).For q-Hahn TASEP and its degenerations (q-TASEP and directed beta polymer) we realize the transposition ν n ↔ ν n+1 as an explicit Markov swap operator acting on the single particle x n (t).For beta polymer, the swap operator can be interpreted as a simple modification of the lattice on which the polymer is considered.Our main tools are Markov duality and contour integral formulas for joint moments.In particular, our constructions lead to a continuous time Markov process Q (t) preserving the time t distribution of the q-TASEP (with step initial configuration, where t ∈ R >0 is fixed).The dual system is a certain transient modification of the stochastic q-Boson system.We identify asymptotic survival probabilities of this transient process with q-moments of the q-TASEP, and use this to show the convergence of the process Q (t) with arbitrary initial data to its stationary distribution.Setting q = 0, we recover the results about the usual TASEP established recently in [arXiv:1907.09155]by a different approach based on Gibbs ensembles of interlacing particles in two dimensions.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".