Martin Hairer, Seiichiro Kusuoka, Hirotatsu Nagoji
{"title":"Singularity of solutions to singular SPDEs","authors":"Martin Hairer, Seiichiro Kusuoka, Hirotatsu Nagoji","doi":"arxiv-2409.10037","DOIUrl":null,"url":null,"abstract":"Building on the notes [Hai17], we give a sufficient condition for the\nmarginal distribution of the solution of singular SPDEs on the $d$-dimensional\ntorus to be singular with respect to the law of the Gaussian measure induced by\nthe linearised equation. As applications we obtain the singularity of the\n$\\Phi^4_3$-measure with respect to the Gaussian free field measure and the\nborder of parameters for the fractional $\\Phi^4$-measure to be singular with\nrespect to the Gaussian free field measure. Our approach is applicable to quite\na large class of singular SPDEs.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"27 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10037","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Building on the notes [Hai17], we give a sufficient condition for the
marginal distribution of the solution of singular SPDEs on the $d$-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
$\Phi^4_3$-measure with respect to the Gaussian free field measure and the
border of parameters for the fractional $\Phi^4$-measure to be singular with
respect to the Gaussian free field measure. Our approach is applicable to quite
a large class of singular SPDEs.