Construction of Φ4 3 diagrams for pedestrians

Jean Christophe Mourrat; Hendrik Weber; Weijun Xu

doi:10.1007/978-3-319-66839-0_1

Construction of Φ⁴ ₃ diagrams for pedestrians

Jean Christophe Mourrat, Hendrik Weber, Weijun Xu

Department of Mathematical Sciences

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

32 Citations (SciVal)

Abstract

We aim to give a pedagogic and essentially self-contained presentation of the construction of various stochastic objects appearing in the dynamical Φ⁴ ₃ model. The construction presented here is based on the use of paraproducts. The emphasis is on describing the stochastic objects themselves rather than introducing a solution theory for the equation.

Original language	English
Title of host publication	From Particle Systems to Partial Differential Equations, PSPDE IV
Editors	P. Gonçalves, A. Soares
Place of Publication	New York, U. S. A.
Publisher	Springer New York
Pages	1-46
Number of pages	46
ISBN (Print)	9783319668383
DOIs	https://doi.org/10.1007/978-3-319-66839-0_1
Publication status	Published - 1 Jan 2017
Event	4th International conference on Particle Systems and Partial Differential Equations, PSPDE 2015 - Braga, Portugal Duration: 16 Dec 2015 → 18 Dec 2015

Publication series

Name	Springer Proceedings in Mathematics & Statistics
Volume	209

Conference

Conference	4th International conference on Particle Systems and Partial Differential Equations, PSPDE 2015
Country/Territory	Portugal
City	Braga
Period	16/12/15 → 18/12/15

Funding

Acknowledgements We are grateful to the very careful referees for their detailed and constructive criticisms, which led to many improvements over the whole paper. We were particularly impressed that one of the referees’ reports turned out to be longer than our paper itself! JCM is partially supported by the ANR Grant LSD (ANR-15-CE40-0020-03). HW is supported by the Royal Society through the University Research Fellowship UF140187. WX is supported by the EPSRC through the fellowship EP/N021568/1.

Keywords

Feynman diagrams
Paraproducts
Singular stochastic PDEs
Stochastic quantisation

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-319-66839-0_1

Cite this

Construction of Φ⁴ ₃ diagrams for pedestrians. / Mourrat, Jean Christophe; Weber, Hendrik; Xu, Weijun.
From Particle Systems to Partial Differential Equations, PSPDE IV. ed. / P. Gonçalves; A. Soares. New York, U. S. A.: Springer New York, 2017. p. 1-46 (Springer Proceedings in Mathematics & Statistics; Vol. 209).

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

Mourrat, JC, Weber, H & Xu, W 2017, Construction of Φ⁴ ₃ diagrams for pedestrians. in P Gonçalves & A Soares (eds), From Particle Systems to Partial Differential Equations, PSPDE IV. Springer Proceedings in Mathematics & Statistics, vol. 209, Springer New York, New York, U. S. A., pp. 1-46, 4th International conference on Particle Systems and Partial Differential Equations, PSPDE 2015, Braga, Portugal, 16/12/15. https://doi.org/10.1007/978-3-319-66839-0_1

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