Gaussian Fields

Roland Bauerschmidt, David C. Brydges, Gordon Slade

Research output: Chapter in Book/Report/Conference proceedingChapter


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.

Original languageEnglish (US)
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Number of pages8
StatePublished - 2019

Publication series

NameLecture Notes in Mathematics
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692


  • Covariance
  • Cumulants
  • Gaussian integration
  • Wick’s lemma

ASJC Scopus subject areas

  • Algebra and Number Theory


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