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KPZ equation from a class of nonlinear SPDEs in infinite volume

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arxiv 2507.10545 v4 pith:FSN7C7H2 submitted 2025-07-14 math.PR math-phmath.APmath.MP

Kevin Yang This is my paper
classification math.PRmath-phmath.APmath.MP
keywords equationspdesclassinfinitenonlinearvolumeanalysiscontinuum
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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.

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    math.PR 2026-05 unverdicted novelty 7.0 of 10

    Establishes weak universality for reaction-diffusion SPDEs with long-range noise via convergence to long-range dynamical Phi^p model using adapted multiindex regularity structures in the subcritical regime.

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