Apparaît dans les collections : Stochastic partial differential equations / Equations aux dérivées partielles stochastiques, Exposés de recherche
I will present some recent results on global solutions to singular SPDEs on $\mathbb{R}^d$ with cubic nonlinearities and additive white noise perturbation, both in the elliptic setting in dimensions $d=4,5$ and in the parabolic setting for $d=2,3$. A motivation for considering these equations is the construction of scalar interacting Euclidean quantum field theories. The parabolic equations are related to the $\Phi^4_d$ Euclidean quantum field theory via Parisi-Wu stochastic quantization, while the elliptic equations are linked to the $\Phi^4_{d-2}$ Euclidean quantum field theory via the Parisi--Sourlas dimensional reduction mechanism. We prove existence for the elliptic equations and existence, uniqueness and coming down from infinity for the parabolic equations. Joint work with Massimiliano Gubinelli.
De Dalia Terhesiu
De Isabelle Gallagher
![[1247] Dérivation de l'équation de Boltzmann en temps long à partir d'une dynamique de sphères dures](/media/cache/video_light/uploads/video/SeminaireBourbaki.png)