English

Discrete RG flow of a hierarchical singular SPDE

Probability 2026-03-19 v1

Abstract

This paper illustrates the Renormalisation Group (RG) approach to singular SPDEs following a framework introduced by Kupiainen \cite{Kupiainen2016}. We study a linear elliptic SPDE with a hierarchical Laplace operator and multiplicative noise, in two dimensions. Although this model is a significant simplification, it captures the core mechanisms of the RG method in a transparent setting. Particular emphasis is placed on the dynamical system governing the flow of the effective force coefficients, the central object of the RG method.

Keywords

Cite

@article{arxiv.2603.17177,
  title  = {Discrete RG flow of a hierarchical singular SPDE},
  author = {Leonard Ferdinand and Simon Gabriel},
  journal= {arXiv preprint arXiv:2603.17177},
  year   = {2026}
}

Comments

32 pages, 1 figure