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.
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References
P. Billingsley, Probability and Measure, 3rd edn. (Wiley, New York, 1995)
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. 7–93
G.B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd edn. (Wiley, New York, 1999)
M. Salmhofer, Renormalization: An Introduction (Springer, Berlin, 1999)
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Bauerschmidt, R., Brydges, D.C., Slade, G. (2019). Gaussian Fields. In: Introduction to a Renormalisation Group Method. Lecture Notes in Mathematics, vol 2242. Springer, Singapore. https://doi.org/10.1007/978-981-32-9593-3_2
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DOI: https://doi.org/10.1007/978-981-32-9593-3_2
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Publisher Name: Springer, Singapore
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Online ISBN: 978-981-32-9593-3
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