Singularity of solutions to singular SPDEs
Probability
2026-02-03 v2
Abstract
Building on the notes [Hai17], we give a sufficient condition for the marginal distribution of the solution of singular SPDEs on the -dimensional torus to be singular with respect to the law of the Gaussian measure induced by the linearised equation. As applications we obtain the singularity of the -measure with respect to the Gaussian free field measure and the border of parameters for the fractional -measure to be singular with respect to the Gaussian free field measure. Our approach is applicable to quite a large class of singular SPDEs.
Keywords
Cite
@article{arxiv.2409.10037,
title = {Singularity of solutions to singular SPDEs},
author = {Martin Hairer and Seiichiro Kusuoka and Hirotatsu Nagoji},
journal= {arXiv preprint arXiv:2409.10037},
year = {2026}
}