Related papers: A random matrix model with non-pairwise contracted…
A non-unitary version of quantum scattering is studied via an exactly solvable toy model. The model is merely asymptotically local since the smooth path of the coordinate is admitted complex in the non-asymptotic domain. At any real…
We introduce a new method, based on the recently developed random tensor theory, to study the p-spin glass model with non-Gaussian, correlated disorder. Using a suitable generalization of Gurau's theorem on the universality of the large N…
We study the dimer and Ising models on a finite planar weighted graph with periodic-antiperiodic boundary conditions, i.e. a graph $\Gamma$ in the Klein bottle $K$. Let $\Gamma_{mn}$ denote the graph obtained by pasting $m$ rows and $n$…
The Hubbard model is used to study an electronic system at half filling. Starting from a functional integral representation the spin-up Grassmann field is integrated out. It is shown that the resulting spinless fermion theory has an…
We propose a one-dimensional nonintegrable spin model with local interactions that covers Dyson's three symmetry classes (classes A, AI, and AII) depending on the values of parameters. We show that the nearest-neighbor spacing distribution…
Colored tensor models generalize matrix models in arbitrary dimensions yielding a statistical theory of random higher dimensional topological spaces. They admit a 1/N expansion dominated by graphs of spherical topology. The simplest tensor…
We explore correlator product states for the approximation of correlated wavefunctions in arbitrary dimensions. We show that they encompass many interesting states including Laughlin's quantum Hall wavefunction, Huse and Elser's frustrated…
Many popular random partition models, such as the Chinese restaurant process and its two-parameter extension, fall in the class of exchangeable random partitions, and have found wide applicability in model-based clustering, population…
One-dimensional topological gravity is defined as a Gaussian integral as its partition function. The Gaussian integral supplies a toy model as a simpler version of one-matrix model that is well known to provide a description of…
Tensor models are natural generalizations of matrix models. The interactions and observables in the case of unitary invariant models are generalizations of matrix traces. Some notable interactions in the literature include the melonic ones,…
Matrix models are a promising candidate for a nonperturbative formulation of the superstring theory. It is possible to study how the standard model and other phenomenological models appear from the matrix model, and estimate the probability…
Mathematical models are sometime given as functions of independent input variables and equations or inequations connecting the input variables. A probabilistic characterization of such models results in treating them as functions with…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
We study the statistical mechanics of random surfaces generated by NxN one-matrix integrals over anti-commuting variables. These Grassmann-valued matrix models are shown to be equivalent to NxN unitary versions of generalized Penner matrix…
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…
Matrix models have phase transitions in which distributions of variables change topologically like the Gross-Witten-Wadia transition. In a recent study, similar splitting-merging behavior of distributions of dynamical variables was observed…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
Motivated by recent efforts to analyze corrections to Weinberg's relations for the scattering length and effective range in the presence of a near-threshold bound state, we play around with an instructive toy model for non-relativistic…
We discuss the utility of analytical and numerical investigation of spin models, in particular spin glasses, on ordinary ``thin'' random graphs (in effect Feynman diagrams) using methods borrowed from the ``fat'' graphs of two dimensional…
We discuss recently discovered links of the statistical models of normal random matrices to some important physical problems of pattern formation and to the quantum Hall effect. Specifically, the large $N$ limit of the normal matrix model…