Gaussian Fields

Roland Bauerschmidt; David C. Brydges; Gordon Slade

doi:10.1007/978-981-32-9593-3_2

Gaussian Fields

Roland Bauerschmidt, David C. Brydges, Gordon Slade

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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.

Original language	English (US)
Title of host publication	Lecture Notes in Mathematics
Publisher	Springer Verlag
Pages	29-36
Number of pages	8
DOIs	https://doi.org/10.1007/978-981-32-9593-3_2
State	Published - 2019

Publication series

Name	Lecture Notes in Mathematics
Volume	2242
ISSN (Print)	0075-8434
ISSN (Electronic)	1617-9692

Keywords

Covariance
Cumulants
Gaussian integration
Wick’s lemma

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1007/978-981-32-9593-3_2

Cite this

@inbook{6bf61f21f0914347ae25491166575505,

title = "Gaussian Fields",

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{\textquoteright}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 = "Covariance, Cumulants, Gaussian integration, Wick{\textquoteright}s lemma",

author = "Roland Bauerschmidt and Brydges, {David C.} and Gordon Slade",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Singapore Pte Ltd.",

year = "2019",

doi = "10.1007/978-981-32-9593-3_2",

language = "English (US)",

series = "Lecture Notes in Mathematics",

publisher = "Springer Verlag",

pages = "29--36",

booktitle = "Lecture Notes in Mathematics",

}

TY - CHAP

T1 - Gaussian Fields

AU - Bauerschmidt, Roland

AU - Brydges, David C.

AU - Slade, Gordon

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Covariance

KW - Cumulants

KW - Gaussian integration

KW - Wick’s lemma

UR - http://www.scopus.com/inward/record.url?scp=85074650939&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85074650939&partnerID=8YFLogxK

U2 - 10.1007/978-981-32-9593-3_2

DO - 10.1007/978-981-32-9593-3_2

M3 - Chapter

AN - SCOPUS:85074650939

T3 - Lecture Notes in Mathematics

SP - 29

EP - 36

BT - Lecture Notes in Mathematics

PB - Springer Verlag

ER -

Gaussian Fields

Abstract

Publication series

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this