TY - BOOK
AU - Gurau, Razvan
TI - Random tensors
SN - 9780198787938
U1 - 530.143
PY - 2017///
CY - New York
PB - Oxford University Press
KW - Random matrices
KW - Calculus of tensors
KW - Quantum field theory
KW - Geometric quantization
KW - Tensor fields
KW - Random sets
N1 - Includes bibliographical references and index
N2 - 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
ER -