02321nam a22002657a 4500999001700000008004100017020002500058082001800083100001800101245001900119250001200138260004800150300003400198365001900232504005100251520145900302650002001761650002401781650002501805650002701830650001801857650001601875942001201891952015201903 c29521d29521190525b xxu||||| |||| 00| 0 eng d a9780198787938c(hbk) a530.143 bGUR aGurau, Razvan aRandom tensors a1st ed. a New York :bOxford University Press,c2017 ax, 333 p. :bill. ;c25.4 cm. aGBPb67.50d00 aIncludes bibliographical references and index. aThis 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 aRandom matrices aCalculus of tensors aQuantum field theory aGeometric quantization aTensor fields aRandom sets 2ddccBK 00102ddc406530_143000000000000_GUR70939744aDAIICTbDAIICTd2019-05-24eBaroda Book Corporationg6372.00o530.143 GURp031935r2019-05-25yBK