arXiv subjects

Y. Bruned

Publications and source records attributed to Y. Bruned.

3 recordsLinked to original sources

arXiv2023

Random models for singular SPDEs

We give a proof of the convergence of the BHZ renormalized model associated with the generalized (KPZ) equation that does not require the full strength of the BPHZ renormalisation. Our approach is based on a convenient form of chaos decomposition. The other key ingredient is a generalisation of the Hairer-Quastel convergence theorem for Feynman diagrams with certain decorations encoding Taylor remainders. With these ideas we are able to construct the model for the generalised KPZ equation.

math.PR↗

arXiv2021

Locality for singular stochastic PDEs

This work deals with singular stochastic PDEs driven by non-translation invariant differential operators. We describe the renormalized equation for a very large class of spacetime dependent renormalization schemes. Our approach bypasses in particular the use of decorated trees with extended decorations.

math.AP↗

arXiv2021

Parametrization of renormalized models for singular stochastic PDEs

Let $\mathscr{T}$ be the regularity structure associated with a given system of singular stochastic PDEs. The paracontrolled representation of the $\sf \Pi$ map provides a linear parametrization of the nonlinear space of admissible models $\sf M=(g,\Pi)$ on $\mathscr{T}$, in terms of the family of para-remainders used in the representation. We give an explicit description of the action of the most general class of renormalization schemes presently available on the parametrization space of the space of admissible models. The action is particularly simple for renormalization schemes associated with degree preserving preparation maps; the BHZ renormalization scheme has that property.

math.PR↗