## Brazilian Journal of Probability and Statistics

- Braz. J. Probab. Stat.
- Volume 29, Number 2 (2015), 175-210.

### Introduction to regularity structures

#### Abstract

These are short notes from a series of lectures given at the University of Rennes in June 2013, at the University of Bonn in July 2013, at the XVIIth Brazilian School of Probability in Mambucaba in August 2013, and at ETH Zurich in September 2013. They give a concise overview of the theory of regularity structures as exposed in the article [*Invent. Math.* DOI: 10.1007/s00222-014-0505-4]. In order to allow to focus on the conceptual aspects of the theory, many proofs are omitted and statements are simplified. We focus on applying the theory to the problem of giving a solution theory to the stochastic quantisation equations for the Euclidean $\Phi^{4}_{3}$ quantum field theory.

#### Article information

**Source**

Braz. J. Probab. Stat. Volume 29, Number 2 (2015), 175-210.

**Dates**

First available in Project Euclid: 15 April 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.bjps/1429105588

**Digital Object Identifier**

doi:10.1214/14-BJPS241

**Mathematical Reviews number (MathSciNet)**

MR3336866

**Zentralblatt MATH identifier**

1316.81061

**Keywords**

Stochastic PDEs regularity structures renormalisation

#### Citation

Hairer, Martin. Introduction to regularity structures. Braz. J. Probab. Stat. 29 (2015), no. 2, 175--210. doi:10.1214/14-BJPS241. https://projecteuclid.org/euclid.bjps/1429105588.