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The Renormalization Group and Self-avoiding Walk

  • David BrydgesEmail author
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2144)

Abstract

These notes describe an application of the renormalization group to a continuous time weakly self-avoiding walk on a four dimensional lattice. The description includes
  • the connection between the local time of continuous time random walk and the massless free field;

  • one of the several formalisms by which the Wilson Renormalisation Group has become the basis for mathematical proof;

  • parts of a proof that there are \(\log ^{\frac{1} {4} }\) corrections in the susceptibility for the four dimensional Edwards model on a lattice with weak coupling.

Keywords

Renormalisation Group Order Perturbation Theory Gaussian Field Continuous Time Random Walk Grassmann Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work was supported in part by NSERC of Canada. Marek Biskup, Roman Kotecký and Martin Slowik helped me write these notes, asking many questions that led to corrections and improvements, but I enjoy all the credit for errors. My colleagues Gordon Slade and Roland Bauerschmidt may not agree with every equation in these notes but none of them would be here without them. I thank my wife Betty Lu Brydges, for her amused tolerance and patience during all the long time this work has been in progress.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsThe University of British ColumbiaVancouverCanada

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