The Laplace transform of the stationary measure of the open KPZ equation in the shock region

@misc{himwich2026laplace,
  title = {{The Laplace transform of the stationary measure of the open KPZ equation in the shock region}},
  author = {Zoe Himwich and Yizao Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30699},
  eprint = {2610.30699},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30699},
}

TY  - UNPB
TI  - The Laplace transform of the stationary measure of the open KPZ equation in the shock region
AU  - Zoe Himwich
AU  - Yizao Wang
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.30699
UR  - https://arxiv.org/abs/2610.30699
AB  - The stationary increment measure of the open Kardar-Parisi-Zhang equation on a bounded interval can be represented as the independent sum of a Brownian motion and another process defined via an explicit Radon-Nikodym derivative with respect to the measure induced by a Brownian motion. In the fan region, its finite-dimensional Laplace transform was previously expressed in terms of the continuous dual Hahn process. The main contribution here consists of computing the finite-dimensional Laplace transform for a range of parameters in the shock region by an analytic continuation argument. As an application, we provide a direct proof of the convergence of the finite-dimensional distributions of the increment height function of open WASEP under the stationary measure in the shock region, by computing the convergence of finite-dimensional Laplace transform without relating to the open KPZ equation.
ER  -