Random Tensors
Răzvan Gheorghe Gurău
Abstract
This book presents a self-contained, ab initio introduction to random tensors. The book is divided into two parts. The first part introduces the general framework and the main results on random tensors. The second part presents in detail specific examples of random tensors models. The book presents both asymptotic results (or perturbative, in the physics literature) and constructive (non perturbative) results in full detail. The book is suitable for readers unfamiliar with the field. The material presented is divided into three broad categories of results. The first category connects random te ... More
This book presents a self-contained, ab initio introduction to random tensors. The book is divided into two parts. The first part introduces the general framework and the main results on random tensors. The second part presents in detail specific examples of random tensors models. The book presents both asymptotic results (or perturbative, in the physics literature) and constructive (non perturbative) results in full detail. The book is suitable for readers unfamiliar with the field. The material presented is divided into three broad categories of results. The first category connects random tensors to topological spaces, Euclidean dynamical triangulations and random geometry. The second category consists of perturbative results on random tensors. It contains the 1/N expansion, the enumeration of graphs of fixed degree, the continuum limit, the double scaling limit as well as the study of phase transitions and symmetry breaking in tensor models. The results in the third category are non perturbative: the proof of the universality of Gaussian tensor measures and the construction of quartically perturbed Gaussian measure. These results are obtained using methods from enumerative combinatorics, probability theory and constructive field theory. Random tensors generalize random matrices and provide a framework for the study of random geometries in any dimension relevant for conformal field theory, statistical physics and quantum gravity.
Keywords:
random tensors,
1/N expansion,
random geometry,
dynamical triangulations,
quantum gravity,
enumerative combinatorics,
probability theory,
constructive field theory
Bibliographic Information
| Print publication date: 2016 |
Print ISBN-13: 9780198787938 |
| Published to Oxford Scholarship Online: January 2017 |
DOI:10.1093/acprof:oso/9780198787938.001.0001 |
Authors
Affiliations are at time of print publication.
Răzvan Gheorghe Gurău, author
Researcher, Centre de Physique Théorique, École Polytechnique, CNRS, Université Paris-Saclay, France
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