Parameter Permutation Symmetry in Particle Systems and Random Polymers
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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 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 j , j n, in a symmetric way. A transposition n 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 n 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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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 | 0.001 |
| 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