相关论文: Solutions of matrix models in the DIII generator e…

We study a two-species partially asymmetric exclusion process where the left boundary is permeable for the `slower' species but the right boundary is not. We find a matrix product solution for the stationary state, and the exact stationary…

In this paper, we study a double scaling limit of two multi-matrix models: the $U(N)^2 \times O(D)$-invariant model with all quartic interactions and the bipartite $U(N) \times O(D)$-invariant model with tetrahedral interaction ($D$ being…

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…

It is shown how to construct a basis in which two arbitrary complex antisymmetric matrices C and C' acquire simultaneously canonical forms. The present construction is not restricted by any conditions on properties of the C^+C' matrix.…

The three-dimensional complexified exteriour bundle $C \otimes \Lambda(R^3)$ is proposed as a geometric interpretation of electroweak doublets of Dirac fermions. The Dirac equation on this bundle allows a staggered discretization on a…

Recently, a two-matrix-model with a new type of interaction [1] has been introduced and analyzed using bi-orthogonal polynomial techniques. Here we present the complete 1/N^2 expansion for the formal version of this model, following the…

Two problems of the Standard Model, associated with the introduction of non-gauge interactions and with the introduction of an electromagnetic field as a linear combination of fields on which various gauge groups are implemented, are…

We describe a general approach for computing generators for elimination ideals associated with matrix and hypermatrix spectral decomposition constraints. We derive from these generators iterative procedures for approximating the spectral…

We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems, via a common generalization in terms of random bipartite graphs. Our algorithm…

In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…

We provide an overview of the diffusion model as a method to generate new samples. Generative models have been recently adopted for tasks such as art generation (Stable Diffusion, Dall-E) and text generation (ChatGPT). Diffusion models in…

The phase diagram of the two-dimensional ANNNI model has long been theoretically debated. Extremely long structural correlations and relaxation times further result in numerical simulations making contradictory predictions. Here, we…

Coupled asymmetric double well ($a\phi^2-b\phi^3+c\phi^4$) one-dimensional potentials arise in the context of first order phase transitions both in condensed matter physics and field theory. Here we provide an exhaustive set of exact…

The steady states of three families of one-dimensional non-equilibrium models with open boundaries, first proposed in [22], are studied using a matrix product formalism. It is shown that their associated quadratic algebras have…

In this work we obtain the planar free energy for the Hermitian one-matrix model with various choices of the potential. We accomplish this by applying an approach that bypasses the usual diagonalization of the matrices and the introduction…

We present a class of matrix models which can be written as double series in the projective Schur functions.

Random matrices in the large N expansion and the so-called double scaling limit can be used as toy models for quantum gravity: 2D quantum gravity coupled to conformal matter. This has generated a tremendous expansion of random matrix…

In arXiv:1003.4694, we proposed two models of M-theory, Hermitian 3-algebra model and Lie 3-algebra model. In this paper, we study the Lie 3-algebra model with a Lorentzian Lie 3-algebra. This model is ghost-free despite the Lorentzian…

Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we…

The D=0 matrix model is reformulated as a 2d nonlocal quantum field theory. The interactions occur on the one-dimensional line of hermitian matrix eigenvalues. The field is conjugate to the density of matrix eigenvalues which appears in the…