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Pré-Publication, Document De Travail Année : 2023

Global harmonic analysis for Φ 4 3 on closed Riemannian manifolds

Résumé

Following Parisi & Wu's paradigm of stochastic quantization, we constructed in [6] a Φ 4 measure on an arbitrary compact, boundaryless, Riemannian manifold as an invariant measure of a singular stochastic partial differential equation. The present work is a companion to [6]. We describe here in detail the harmonic and microlocal analysis tools that we used. We also introduce some new tools to treat the vectorial Φ 4 3 model. This relies on a new Cole-Hopf transform involving random bundle maps. We do not aim here for the greatest generality; rather, we tried to keep our exposition relatively self-contained and pedagogical enough in the hope that the techniques we show can be used in other settings.
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Dates et versions

hal-04128173 , version 1 (14-06-2023)

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I Bailleul, N V Dang, L Ferdinand, Tat Dat Tô. Global harmonic analysis for Φ 4 3 on closed Riemannian manifolds. 2023. ⟨hal-04128173⟩
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