Paracontrolled distributions and the 3-dimensional stochastic quantization equation
By Rémi Catellier, K. Chouk. Annals of Probability, 2013
163 citations recorded by the source corpus.
We prove the existence and uniqueness of a local solution to the periodic renormalized $\Phi^4_3$ model of stochastic quantisation using the method of controlled distributions introduced recently by Imkeller, Gubinelli and Perkowski ("Paraproducts, rough paths and controlled distributions", arXiv:1210.2684)
Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance
View Paper: https://www.semanticscholar.org/paper/766541b31b00a00ff9119748653cc74afbe954d9
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Jean-Christophe Mourrat
- Felix Otto
- Ismaël F. Bailleul
- Frédéric Bernicot
- Hendrik Weber
- P. Tsatsoulis
- Markus Tempelmayr
- P. Linares
In Computational Theory and Mathematics
- Jean-Christophe Mourrat
- Felix Otto
- Hendrik Weber
- Frédéric Bernicot
- Ismaël F. Bailleul
- P. Tsatsoulis
- Markus Tempelmayr
- P. Linares
In Finance
- Jean-Christophe Mourrat
- Hendrik Weber
- Herbert Koch
- Tadahiro Oh
- Ismaël F. Bailleul
- Frédéric Bernicot
- Massimiliano Gubinelli
- Felix Otto
Citations in the corpus
- The Dynamic $${\Phi^4_3}$$Φ34 Model Comes Down from Infinity (2016, methodology): “A similar local theory was already presented in [5] in a slightly different formulation (see Remark 1.”
- HIGH ORDER PARACONTROLLED CALCULUS (2016, background): “While this kind of approach may seem far from being as powerful as Hairer’s machinery, the first order paracontrolled approach to singular stochastic PDEs has been successful in recovering and extending a number of results that can be proved within the setting of regularity structures, on the parabo”
- Renormalization Group and Stochastic PDEs (2016, background): “The latter case was also addressed by Catellier and Chouk [2] based on the theory of paracontrolled distributions developed in [3].”
- A diagram-free approach to the stochastic estimates in regularity structures (2021, background): “Kupiainen appealed to Wilsonian renormalization [27, 28] to treat some semi-linear SPDEs.”
- Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity (2018, methodology): “On the other hand, the theory of paracontrolled distributions has revealed itself as an effective method for a restricted class of singular SPDEs [18, 38, 1, 90, 52, 4, 5, 65, 28, 54, 53, 35, 79, 16].”