Renormalised Models for Variable Coefficient Singular SPDEs

Lucas Broux; Harprit Singh; Rhys Steele

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arXiv · 2507.06851

Renormalised Models for Variable Coefficient Singular SPDEs

Lucas Broux·Harprit Singh·Rhys Steele

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Abstract

In this work we prove convergence of renormalised models in the framework of regularity structures [Hai14] for a wide class of variable coefficient singular SPDEs in their full subcritical regimes. In particular, we provide for the first time an extension of the main results of [CH16, HS24, BH23] beyond the translation invariant setting. In the non-translation invariant setting, it is necessary to introduce renormalisation functions rather than renormalisation constants. We show that under a very general assumption, which we prove covers the case of second order parabolic operators, these renormalisation functions can be chosen to be local in the sense that their space-time dependence enters only through a finite order jet of the coefficient field of the differential operator at the given space-time point. Furthermore we show that the models we construct depend continuously on the coefficient field.

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Lucas Broux, Harprit Singh, Rhys Steele. 2025-07-09. Renormalised Models for Variable Coefficient Singular SPDEs. https://arxiv.org/abs/2507.06851

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