Gurau R. Random Tensors

Oxford: Oxford University Press, 2017. — 345 p.Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics.Introduction
Toolbox for random tensors
Preliminaries
Generalities on edge colored graphs
The classification of edge colored graphs
Melonic graphs
The universality theorem
Random tensor models
A digest of matrix models
The perturbative expansion of tensor models
The quartic tensor model
The double scaling limit
Symmetry breaking
Conclusions
Appendices
Appendix A The Weingarten functions revisited
Appendix B Probability measures
Appendix C Borel summability
Appendix D The BKAR formula
Bibliography
Index