Discrete RG flow of a hierarchical singular SPDE

TL;DR

This paper applies the Renormalisation Group approach to a simplified hierarchical singular SPDE in two dimensions, focusing on the flow of effective force coefficients to understand the core mechanisms of the RG method.

Contribution

It demonstrates the RG method's application to a hierarchical singular SPDE, highlighting the dynamics of effective force coefficients in a transparent setting.

Findings

RG flow of effective force coefficients analyzed

Hierarchical Laplace operator used in 2D model

Simplified model captures core RG mechanisms

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.