Integration by parts and invariant measure for KPZ
Probability
2025-04-09 v2 Mathematical Physics
math.MP
Abstract
Using Stein's method and a Gaussian integration by parts, we provide a direct proof of the known fact that drifted Brownian motions are invariant measures (modulo height) for the KPZ equation.
Keywords
Cite
@article{arxiv.2409.08465,
title = {Integration by parts and invariant measure for KPZ},
author = {Yu Gu and Jeremy Quastel},
journal= {arXiv preprint arXiv:2409.08465},
year = {2025}
}
Comments
v2, 17 pages, revised version. There was a mistake in Lemma 4.3 of v1 which we fixed. The rest of the proof stays the same