### Abstract

We aim to give a pedagogic and essentially self-contained presentation of the construction of various stochastic objects appearing in the dynamical Φ^{4} _{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 |
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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 | |

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 |
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Volume | 209 |

### Conference

Conference | 4th International conference on Particle Systems and Partial Differential Equations, PSPDE 2015 |
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Country | Portugal |

City | Braga |

Period | 16/12/15 → 18/12/15 |

### Keywords

- Feynman diagrams
- Paraproducts
- Singular stochastic PDEs
- Stochastic quantisation

### ASJC Scopus subject areas

- Mathematics(all)

## Cite this

Mourrat, J. C., Weber, H., & Xu, W. (2017). Construction of Φ

^{4}_{3}diagrams for pedestrians. In P. Gonçalves, & A. Soares (Eds.),*From Particle Systems to Partial Differential Equations, PSPDE IV*(pp. 1-46). (Springer Proceedings in Mathematics & Statistics; Vol. 209). Springer New York. https://doi.org/10.1007/978-3-319-66839-0_1