[Submitted on 14 Jul 2025 (v1), last revised 21 Jul 2026 (this version, v4)]

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Abstract:We study a general class of nonlinear Ginzburg-Landau SPDEs in infinite volume under weak nonlinearity scaling and with non-equilibrium initial data. We derive the KPZ equation as a continuum limit of these equations. This makes rigorous the original derivation of the KPZ equation from physics in the full-space setting, which was a problem posed by Hairer-Quastel '18. Our analysis is based on a stochastic heat kernel for a linearization of said SPDEs.

Submission history

From: Kevin Yang [view email]
[v1] Mon, 14 Jul 2025 17:59:32 UTC (77 KB)
[v2] Fri, 5 Sep 2025 13:15:06 UTC (78 KB)
[v3] Fri, 26 Dec 2025 20:06:58 UTC (79 KB)
[v4] Tue, 21 Jul 2026 00:54:55 UTC (80 KB)

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