Hyperbolic Anderson model with time-independent rough noise: Gaussian fluctuations
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Bibliographic record
Abstract
In this article, we study the hyperbolic Anderson model in dimension 1, driven by a time-independent rough noise, i.e. the noise associated with the fractional Brownian motion of Hurst index H∈(1∕4,1∕2). We prove that, with appropriate normalization and centering, the spatial integral of the solution converges in distribution to the standard normal distribution, and we estimate the speed of this convergence in the total variation distance. We also prove the corresponding functional limit result. Our method is based on a version of the second-order Gaussian Poincaré inequality developed recently in [29], and relies on delicate moment estimates for the increments of the first and second Malliavin derivatives of the solution. These estimates are obtained using a connection with the wave equation with delta initial velocity, a method which is different than the one used in [29] for the parabolic Anderson model.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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