@inbook{8cbfc62e8047414183a77b141a055677,

title = "The Hierarchical Model",

abstract = "We define a hierarchical Gaussian field in a way that is motivated by the finite-range decomposition of the Gaussian free field. The hierarchical Gaussian free field is a hierarchical field that has comparable large distance behaviour to the lattice Gaussian free field. We explicitly construct a version of the hierarchical Gaussian field and verify that it has the desired properties. We define the hierarchical |φ|4 model and state the main result proved in this book, which gives the critical behaviour of the susceptibility of the 4-dimensional hierarchical |φ|4 model. In preparation for the proof of the main result, we reformulate the hierarchical |φ|4 model as a perturbation of a Gaussian integral.",

keywords = "Hierarchical Gaussian free field, Hierarchical Laplacian, Hierarchical |φ| model",

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_4",

language = "English (US)",

series = "Lecture Notes in Mathematics",

publisher = "Springer Verlag",

pages = "53--65",

booktitle = "Lecture Notes in Mathematics",

}