Related papers: Unitary Integrals and Related Matrix Models
In this paper we obtained several properties that the characteristic polynomials of the unit-primitive matrix satisfy. In addition, using these properties we have shown that the recurrence relation given as in the formula (1) is true. In…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
The restricted Boltzmann machine is a network of stochastic units with undirected interactions between pairs of visible and hidden units. This model was popularized as a building block of deep learning architectures and has continued to…
We generalize three main concepts of Gabor analysis for lattices to the setting of model sets: Fundamental Identity of Gabor Analysis, Janssen's representation of the frame operator and Wexler-Raz biorthogonality relations. Utilizing the…
This short but self-contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen, sub or super-additivity type inequalities are…
We perform a In\"on\"u--Wigner contraction on Gaudin models, showing how the integrability property is preserved by this algebraic procedure. Starting from Gaudin models we obtain new integrable chains, that we call Lagrange chains,…
We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also…
Non-unitarity of the neutrino mixing matrix is expected in many scenarios with physics beyond the Standard Model. Motivated by the search for deviations from unitary, we study two neutrino counting observables: the neutrino-antineutrino…
In this note, we briefly introduce the background and motivation of the collaborative work [arXiv:2508.20797], and provide an outline of the main results. The latter relates to matrix and higher order scalar differential equations satisfied…
We reconsider the simple matrix model description of Hurwitz numbers proposed by S. Natanzon and A. Orlov, which uses the superintegrability property of the complex matrix model, and discuss a way of its possible supersymmetric extension to…
We present a survey of recent results concerning a remarkable class of unitary matrices, the CMV matrices. We are particularly interested in the role they play in the theory of random matrices and integrable systems. Throughout the paper we…
According to the classification scheme of the generalized random matrix ensembles, we present various kinds of concrete examples of the generalized ensemble, and derive their joint density functions in an unified way by one simple formula…
A paper of the first author and Zilke proposed seven combinatorial problems around formulas for the characteristic polynomial and the exponents of an isolated quasihomogeneous singularity. The most important of them was a conjecture on the…
We analyze the neutrino mass matrix entries and their correlations in a probabilistic fashion, constructing probability distribution functions using the latest results from neutrino oscillation fits. Two cases are considered: the standard…
A brief review of the eigenvalue matrix model integrability and superintegrability properties, focused on the simplest, still representative, Gaussian Hermitian case.
Mathematical models are an important tool for neuroscientists. During the last thirty years many papers have appeared on single neuron description and specifically on stochastic Integrate and Fire models. Analytical results have been proved…
We introduce finite mixtures of Ising models as a novel approach to study multivariate patterns of associations of binary variables. Our proposed models combine the strengths of Ising models and multivariate Bernoulli mixture models. We…
In a recent paper, an algorithm has been presented for determining implications between a particular kind of category theoretic property represented by matrices -- the so called `matrix properties'. In this paper we extend this algorithm to…
We review theoretical ideas, problems and implications of different models for neutrino masses and mixing angles. We give a general discussion of schemes with three or more light neutrinos. Several specific examples are analyzed in some…
An overview is given of the experimental neutrino mixing results and types of neutrino models proposed, with special attention to the general features of various GUT models involving intra-family symmetries and horizontal flavor symmetries.…