Integration by parts and invariant measure for KPZ

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.

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