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Gaussian Fields

  • Roland Bauerschmidt
  • David C. Brydges
  • Gordon Slade
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2242)

Abstract

We provide a concise introduction to the basic properties of Gaussian integration. These include Gaussian integration by parts, the connection with the Laplace operator, Wick’s lemma, the characterisation by the Laplace transform, and the computation of cumulants (also called truncated expectations). The fact that the sum of two independent Gaussian fields is also Gaussian is derived, along with the corresponding convolution property which is fundamental for the renormalisation group.

Keywords

Gaussian integration Covariance Wick’s lemma Cumulants 

References

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    D.C. Brydges, Lectures on the renormalisation group, in Statistical Mechanics, ed. by S. Sheffield, T. Spencer. IAS/Park City Mathematics Series, vol. 16 (American Mathematical Society, Providence, 2009), pp. 7–93Google Scholar
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    G.B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd edn. (Wiley, New York, 1999)zbMATHGoogle Scholar
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    M. Salmhofer, Renormalization: An Introduction (Springer, Berlin, 1999)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Roland Bauerschmidt
    • 1
  • David C. Brydges
    • 2
  • Gordon Slade
    • 2
  1. 1.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeCambridgeUK
  2. 2.Department of MathematicsThe University of British ColumbiaVancouverCanada

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