Authors : Hofmanova, Martina (Author of the conference)
CIRM (Publisher )
Abstract :
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
MSC Codes :
35Q40
- PDEs in connection with quantum mechanics
60H15
- Stochastic partial differential equations
81S20
- Stochastic quantization
81T08
- Constructive quantum field theory
35J61
- Semilinear elliptic equations
Additional resources :
https://www.cirm-math.fr/ProgWeebly/Renc1742/Hofmanova.pdf
Film maker : Hennenfent, Guillaume
Language : English
Available date : 22/05/2018
Conference Date : 15/05/2018
Subseries : Research talks
arXiv category : Probability ; Mathematical Physics ; Analysis of PDEs
Mathematical Area(s) : Probability & Statistics ; Mathematical Physics ; PDE
Format : MP4 (.mp4) - HD
Video Time : 00:44:58
Targeted Audience : Researchers
Download : https://videos.cirm-math.fr/2018-05-15_Hofmanova.mp4
|
Event Title : Stochastic partial differential equations / Equations aux dérivées partielles stochastiques Event Organizers : Berglund, Nils ; Debussche, Arnaud ; Delarue, François ; Kuehn, Christian Dates : 14/05/2018 - 18/05/2018
Event Year : 2018
Event URL : https://conferences.cirm-math.fr/1742.html
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
|
See Also
Bibliography