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H 1 Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space

Auteurs : Hofmanova, Martina (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : 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.

    Keywords : singular SPDEs; paracontrolled distributions; global solutions; stochastic quantization; dimensional reduction; semilinear elliptic equations

    Codes MSC :
    35Q40 - PDEs in connection with quantum mechanics
    60H15 - Stochastic partial differential equations
    81S20 - Stochastic quantization
    81T08 - Constructive quantum field theory
    35J61 - Semilinear elliptic equations

    Ressources complémentaires :

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 22/05/2018
      Date de captation : 15/05/2018
      Collection : Research talks ; Partial Differential Equations ; Mathematical Physics ; Probability and Statistics
      Format : MP4
      Durée : 00:44:58
      Domaine : Probability & Statistics ; Mathematical Physics ; PDE
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2018-05-15_Hofmanova.mp4

    Informations sur la rencontre

    Nom de la rencontre : Stochastic partial differential equations / Equations aux dérivées partielles stochastiques
    Organisateurs de la rencontre : Berglund, Nils ; Debussche, Arnaud ; Delarue, François ; Kuehn, Christian
    Dates : 14/05/2018 - 18/05/2018
    Année de la rencontre : 2018
    URL Congrès : https://conferences.cirm-math.fr/1742.html

    Citation Data

    DOI : 10.24350/CIRM.V.19401603
    Cite this video as: Hofmanova, Martina (2018). Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19401603
    URI : http://dx.doi.org/10.24350/CIRM.V.19401603

    Voir aussi


    1. Gubinelli, M., & Hofmanová, M. (2018). Global solutions to elliptic and parabolic Φ4 models in Euclidean space. - https://arxiv.org/abs/1804.11253