Spatial Mollification of the Multilayer Stochastic Heat Equation
Manuscript 12 October 2026 · Online 12 October 2026
Abstract
We give a spatial mollifier construction of the O'Connell-Warren multilayer stochastic heat equation directly from nonintersecting Brownian bridges with coalesced endpoints. Both the fully Wick-ordered exponential of the total path energy and the product of separately Wick-ordered path weights converge to the chaos partition function in every finite Lp norm. The difference between the two approximations is O(epsilon^alpha) for every 0 < alpha < 1. The proof combines the established chaos and intersection-local-time estimates with a mollifier-independent inverse-gap bound for the mutual-path counterterm. All parameters, including the number of layers, are fixed. The comparison rate is not a rate to the limiting field; uniform sample-path convergence and temporal smoothing are not claimed. This supplies the spatial smoothing construction in AIM KPZ item 2.04 (UnsolvedMath AIM-PROBABILITY-0086, imported with the label 22.04). The work relies on and explicitly credits O'Connell and Warren's machinery. It is an AI-assisted, self-audited, unrefereed preprint, without independent peer review, formal verification or an absolute-priority claim.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Complete fixed-parameter proof
- Categories
- math.PR · math.MP
- Manuscript
- 12 October 2026
- Online release
- 12 October 2026
- Version
- 1.0
- License
- Creative Commons Attribution 4.0 International
Files and verification
The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.
Citation
Alper Ferudun, “Spatial Mollification of the Multilayer Stochastic Heat Equation,” EulerSolve Research Papers, AIM-PROBABILITY-0086, 2026. https://doi.org/10.5281/zenodo.23315978.
BibTeX
@misc{ferudun2026multilayerspatial,
author = {Ferudun, Alper},
title = {Spatial Mollification of the Multilayer Stochastic Heat Equation},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/aim-probability-0086/},
doi = {10.5281/zenodo.23315978},
note = {AIM-PROBABILITY-0086; unrefereed preprint}
}