Random tensors
type: Item
instance of: scholarly article
zbMATH Open document ID: 1371.81007
author: R. Gurau
publication date: 2016-10-12T00:00:00Z
Mathematics Subject Classification ID: 81-02
Mathematics Subject Classification ID: 81S25
Mathematics Subject Classification ID: 15B52
Mathematics Subject Classification ID: 00A79
Mathematics Subject Classification ID: 60B20
Mathematics Subject Classification ID: 83C45
Mathematics Subject Classification ID: 60D05
zbMATH DE Number: 6638014
zbMATH Keywords: random tensors
zbMATH Keywords: edge colored graphs
zbMATH Keywords: Melonic graphs
zbMATH Keywords: the continuum limit
zbMATH Keywords: double scaling limit
zbMATH Keywords: quartic tensor model
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1093/acprof:oso/9780198787938.001.0001
OpenAlex ID: W4238800314
DOI: 10.1093/ACPROF:OSO/9780198787938.001.0001
title: Random tensors
review text: This book is a self-contained introductory text to the theory of random tensors. The book presents theory and its applications to physics. This book introduces a framework for studying random geometries in any dimensions. This book shows that many results in random matrices, most notably, Hooft's \(1/N\) expansion can be generalized to higher dimension.NEWLINENEWLINERandom tensor models generalize random matrix models and provide a framework for the study of random geometries. The development of matrix models is one of the most impressive achievements of modern theoretical physics. Generalizing random matrices, random tensors generate Feyman graphs, which can be interpreted as topological spaces.NEWLINENEWLINEThe book consists of three parts. The first part consists of Chapters 2 to 6. In this part, the general framework and the main results on random tensors are introduced. The second part consists of Chapters 7 to 11. In this part, specific examples of random tensor models are discussed. The third part consists of appendices related to Weingarten functions, probability measures, Borel summability and BKAR formula.NEWLINENEWLINEChapter 1 is introductory.NEWLINENEWLINEChapter 2: Preliminaries related to tensors, invariants, edge colored graphs, matrices, connected and disconnected trace invariants, uniqueness of the decomposition on trace invariants, invariant probability measures are discussed. Also representation of invariants as edge colored graphs is introduced.NEWLINENEWLINEChapter 3: In this chapter, the edge colored graphs are studied. It is shown that each graph is a \(D\)-complex dual to a vertex colored triangulation. Also, open graphs and their boundary graphs are discussed. The notion of ``degree'' associated with to a connected edge colored graph are introduced.NEWLINENEWLINEChapter 4: In this chapter, the classification of graphs at fixed degree is given. It is shown that for any fixed degree, one obtains an infinite but exponentially bounded family of…
reviewed by: S. K. Nimbhorkar
description: scientific article; zbMATH DE number 6638014