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Renormalisation in the flow approach for singular SPDEs

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arxiv 2504.04885 v2 pith:LBTK6SXZ submitted 2025-04-07 math.PR math-phmath.APmath.MPmath.RA

Yvain Bruned , Aurélien Minguella This is my paper
classification math.PRmath-phmath.APmath.MPmath.RA
keywords renormalisationansatzflowapproachequationregularityrenormalisedsingular
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In this work, we study the renormalisation of singular SPDEs in the flow approach recently developed by Duch. We introduce a general ansatz based on decorated trees for the solution of the flow equation. The ansatz is renormalised in a recursive way, in the sense of the trees, via local extractions introduced for regularity structures. We derive the renormalised equation from this ansatz and show that the renormalisation scheme is identical to that appearing in the context of regularity structures, thus matching the BPHZ renormalisation.

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  1. Lecture notes on the flow equation approach to singular stochastic PDEs

    math.PR 2025-11 conditional novelty 4.0 of 10

    A scale-by-scale flow equation with suitably chosen counterterms constructs renormalized solutions of fractional elliptic Phi^4 SPDEs throughout the subcritical regime.

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