Bounds on Φ+K: Proof of Theorem 8.2.4

Roland Bauerschmidt, David C. Brydges, Gordon Slade

Research output: Chapter in Book/Report/Conference proceedingChapter


We prove the main estimates on the nonperturbative coordinate of the renormalisation group map. This is the heart of the proof of the main result. One ingredient in the proof of the main estimates consists of the stability estimates which exploit the decay arising from e−g|φ|4. A central ingredient in the proof consists of the crucial contraction which is responsible for the contractive property of the renormalisation group map. The contractive property was used in an essential way to construct the global renormalisation group flow in Chap. 6.

Original languageEnglish (US)
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Number of pages29
StatePublished - 2019

Publication series

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


  • Crucial contraction
  • Renormalisation group map
  • Stability estimate

ASJC Scopus subject areas

  • Algebra and Number Theory


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