Related papers: Quartic Tensor Models
In this text we review a few structural properties of matrix models that should at least partly generalize to random tensor models. We review some aspects of the loop equations for matrix models and their algebraic counterpart for tensor…
This note is a sequel to the previous series "Tensor Track I-III". Assuming some familiarity with the tensor track approach to quantum gravity, we provide a brief introduction to the developments of the last two years and to their…
We extend the study of \emph{melonic} quartic tensor models to models with arbitrary quartic interactions. This extension requires a new version of the loop vertex expansion using several species of intermediate fields and iterated…
Tensor models are generalization of matrix models, and are studied as models of quantum gravity. It is shown that the symmetry of the rank-three tensor models is generated by a hierarchy of n-ary algebras starting from the usual commutator,…
We build constructively the simplest tensor field theory which requires some renormalization, namely the rank three tensor theory with quartic interactions and propagator inverse of the Laplacian on $U(1)^3$. This superrenormalizable tensor…
Tensor models generalize the matrix-model approach to 2-dimensional quantum gravity to higher dimensions. Some models allowing a $1/N$ expansion have been explored, most of them generating branched-polymer geometries. Recently, enhancements…
The attempt of extending to higher dimensions the matrix model formulation of two-dimensional quantum gravity leads to the consideration of higher rank tensor models. We discuss how these models relate to four dimensional quantum gravity…
Random matrix models encode a theory of random two dimensional surfaces with applications to string theory, conformal field theory, statistical physics in random geometry and quantum gravity in two dimensions. The key to their success lies…
Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the…
The general linear model is a universally accepted method to conduct and test multiple linear regression models. Using this model one has the ability to simultaneously regress covariates among different groups of data. Moreover, there are…
Random tensor models can be used as combinatorial devices to generate Euclidean dynamical triangulations. A physical continuum limit of dynamical triangulations requires a suitable generalization of the double-scaling limit of random…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these…
We define in this paper a class of three indices tensor models, endowed with $O(N)^{\otimes 3}$ invariance ($N$ being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor…
Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
Certain families of quantum mechanical models can be described and solved efficiently on a classical computer, including qubit or qudit Clifford circuits and stabilizer codes, free-boson or free-fermion models, and certain rotor and GKP…
Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…
Modular tensor categories are generalizations of the representation categories of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFTs. Although other constructions have since been found,…
Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…
Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…