Work

KPZ equation from a class of nonlinear SPDEs in infinite volume

Year: 2026

Type: article

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 [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.

Source: Probability Theory and Related Fields

DOI: 10.1007/s00440-026-01521-w

Author: Kevin Yang

Institution: University of California, Berkeley

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: National Science Foundation