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<p>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 [<CitationRef CitationID="CR31">31</CitationRef>] in the full-space setting, which was a problem posed in [<CitationRef CitationID="CR27">27</CitationRef>]. Our analysis is based on a stochastic heat kernel for a linearization of said SPDEs.</p>

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KPZ equation from a class of nonlinear SPDEs in infinite volume

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月22日

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  • Kevin Yang

摘要

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 [31] in the full-space setting, which was a problem posed in [27]. Our analysis is based on a stochastic heat kernel for a linearization of said SPDEs.