Related papers: Matrix Models and Large-N Behavior
Non-symmetric rectangular correlation matrices occur in many problems in economics. We test the method of extracting statistically meaningful correlations between input and output variables of large dimensionality and build a toy model for…
Correlation functions of matrix-valued fields are not generally known for massive renormalized field theories. We find the large-N limit of form factors of the (1+1)-dimensional sigma model with SU(N) X SU(N) symmetry. These form factors…
Tensor models and tensor field theories admit a $1/N$ expansion and a melonic large $N$ limit which is simpler than the planar limit of random matrices and richer than the large $N$ limit of vector models. They provide examples of…
Although random tensor models were introduced twenty years ago, it is only in 2011 that Gurau proved the existence of a 1/N expansion. Here we show that there actually is more than a single 1/N expansion, depending on the dimension. These…
In this work we analyze strategies for convolutional neural network scaling; that is, the process of scaling a base convolutional network to endow it with greater computational complexity and consequently representational power. Example…
We propose descriptions of interacting (1,0) supersymmetric theories without gravity in six dimensions in the infinite momentum frame. They are based on the large N limit of quantum mechanics or 1+1 dimensional field theories with SO(N)…
The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…
We investigate a class of models in 1+1 dimensions with four fermion interaction term. At each order of the perturbation expansion, the models are ultraviolet finite and Lorentz non-invariant. We show that for certain privileged values of…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices, we derive a new representation for the…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
We construct quasi-solvable quantum mechanical matrix models by employing two different methods, the one is universal enveloping algebra of Lie superalgebra and the other is N-fold supersymmetry. For the former we examine the q(2) and…
Recent literature suggests that the bigger the model, the more likely it is to converge to similar, ``universal'' representations, despite different training objectives, datasets, or modalities. While this literature shows that there is an…
We investigate the controversial issue of the existence of universality classes describing critical phenomena in three-dimensional statistical systems characterized by a matrix order parameter with symmetry O(2)xO(N) and symmetry-breaking…
The thermodynamics of the O(N) linear and nonlinear sigma models in 3+1 dimensions is studied. We calculate the pressure to next-to-leading order in the 1/N expansion and show that at this order, temperature-independent renormalization is…
Organisms in nature have evolved to exhibit flexibility in face of changes to the environment and/or to themselves. Artificial neural networks (ANNs) have proven useful for controlling of artificial agents acting in environments. However,…
Intertwining relations for $N$-particle Calogero-like models with internal degrees of freedom are investigated. Starting from the well known Dunkl-Polychronakos operators, we construct new kind of local (without exchange operation)…
The first part of these lecture notes is mostly devoted to a comparative discussion of the three basic large $N$ limits, which apply to fields which are vectors, matrices, or tensors of rank three and higher. After a brief review of some…
We construct the {\cal N}=4 supersymmetric nonlinear sigma model in three dimensions which can be expanded in 1/N. We evaluate the effective action at leading order in the 1/N expansion and show the finiteness of the model to this order.