Global Flow: Proof of Theorem 4.2.1

Roland Bauerschmidt, David C. Brydges, Gordon Slade

Research output: Chapter in Book/Report/Conference proceedingChapter


We define the specific norms used to analyse the renormalisation group map, and specify the domain of the map. The choice of norms is based on considerations concerning the typical sizes of the fluctuation and block-spin fields. We state the main estimates on the renormalisation group map in two theorems, and then use these theorems to construct the global renormalisation group flow in the nonperturbative case. The construction requires, in particular, the construction of the critical point. The latter is done via the Bleher–Sinai argument. The results of this chapter reduce our analysis of the 4-dimensional hierarchical model to the proof of the estimates on the renormalisation group map stated in this chapter. The two theorems which state those estimates are proved in the next two chapters.

Original languageEnglish (US)
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Number of pages16
StatePublished - 2019

Publication series

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


  • Bleher–Sinai argument
  • Critical point
  • Renormalisation group flow

ASJC Scopus subject areas

  • Algebra and Number Theory


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