Table of Contents

1 The Renormalisation Group and some Applications

1.1 The lectures of David Brydges

at the 2013 School on Mathematical Statistical Physics

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

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

Date: 2013-08-25 09:32:33 PDT

Author: David Brydges

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