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Renormalization of singular elliptic stochastic PDEs using flow equation

Paweł Duch

Vol. 6 (2025), No. 1, 111–138
Abstract

We develop a solution theory for singular elliptic stochastic PDEs with fractional Laplacian, additive white noise and cubic nonlinearity. The method covers the whole subcritical regime. It is based on the Wilsonian renormalization group theory and the Polchinski flow equation.

Keywords
singular stochastic PDEs, renormalization group, flow equation
Mathematical Subject Classification
Primary: 60H17, 81T17
Milestones
Received: 17 January 2022
Revised: 23 May 2024
Accepted: 21 August 2024
Published: 5 February 2025
Authors
Paweł Duch
EPFL
Lausanne
Switzerland
Faculty of Mathematics and Computer Science
Adam Mickiewicz University in Poznań
Poznań
Poland