Invariant measures for the open KPZ equation: the Gaussian case
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908993510703104 |
|---|---|
| author | Bona-Landry, James |
| author_facet | Bona-Landry, James |
| contents | In [arXiv:2409.08465], Quastel and Gu use Stein's equation and integration by parts to give a direct proof that drifted Brownian motions are stationary (modulo height shifts) for the full-line KPZ equation. In this article, we consider the open KPZ equation with boundary conditions $\partial_x h(t,0) = \partial_x h(t,1) = α$ for a general real parameter $α$, and emulate the approach of Quastel and Gu to provide a similar proof that Brownian motion with constant drift $α$ is invariant (modulo height shifts) in this case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23462 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Invariant measures for the open KPZ equation: the Gaussian case Bona-Landry, James Probability In [arXiv:2409.08465], Quastel and Gu use Stein's equation and integration by parts to give a direct proof that drifted Brownian motions are stationary (modulo height shifts) for the full-line KPZ equation. In this article, we consider the open KPZ equation with boundary conditions $\partial_x h(t,0) = \partial_x h(t,1) = α$ for a general real parameter $α$, and emulate the approach of Quastel and Gu to provide a similar proof that Brownian motion with constant drift $α$ is invariant (modulo height shifts) in this case. |
| title | Invariant measures for the open KPZ equation: the Gaussian case |
| topic | Probability |
| url | https://arxiv.org/abs/2604.23462 |