# index

## Table of Contents

- 1 The Renormalisation Group and some Applications
- 1.1 The lectures of David Brydges
- 1.2 Abstract:
- 1.3 Topics
- 1.3.1 The Edwards model for self-avoiding walk on a d-dimensional lattice
- 1.3.2 log corrections in the susceptibility in four dimensions
- 1.3.3 The massless Gaussian measure and local time isomorphisms
- 1.3.4 Finite range decompositions of Gaussian fields and progressive integration
- 1.3.5 First order perturbation theory and flow of interaction
- 1.3.6 Exact representation as a flow
- 1.3.7 Second order perturbation theory and origin of log corrections

- 1.4 More details on lectures at
- 1.5 Problems

## 1 The Renormalisation Group and some Applications

### 1.1 The lectures of David Brydges

at the 2013 School on Mathematical Statistical Physics

http://www.math.ucla.edu/~biskup/Prague-school-2013/index.html

### 1.2 Abstract:

My goal is to explain the renormalisation group as a rigorous program to understand scaling limits. I will centre the lectures on recent work with Gordon Slade and Roland Bauerschmidt on log corrections in the susceptibility for the four dimensional Edwards model.

### 1.3 Topics

#### 1.3.1 The Edwards model for self-avoiding walk on a d-dimensional lattice

#### 1.3.2 log corrections in the susceptibility in four dimensions

#### 1.3.3 The massless Gaussian measure and local time isomorphisms

#### 1.3.4 Finite range decompositions of Gaussian fields and progressive integration

#### 1.3.5 First order perturbation theory and flow of interaction

#### 1.3.6 Exact representation as a flow

#### 1.3.7 Second order perturbation theory and origin of log corrections

### 1.4 More details on lectures at

#### 1.4.1 BIS2009

D.C. Brydges, J.Z. Imbrie, G. Slade, Functional integral representations for self-avoiding walk. Probability Surveys, 6:34–61, (2009). pdf file posted on my homepage

#### 1.4.2 Ba2013

Roland Bauerschmidt, Decomposition of free fields and structural stability of dynamical systems for renormalization group analysis, PhD Thesis 2013,

#### 1.4.3 Br2007

2007 Park City Summer School, pdf file posted on my homepage

http://www.math.ubc.ca/~db5d/Research/index.html

Chapter in Statistical Mechanics edited by: Scott Sheffield, Massachusetts Institute of Technology, Cambridge, MA, and Thomas Spencer, Institute for Advanced Study, Princeton, NJ

### 1.5 Problems

See problems.pdf