Related papers: Generalizations of some integrals over the unitary…
In order to apply nonstandard methods to modern algebraic geometry, as a first step in this paper we study the applications of nonstandard constructions to category theory. It turns out that many categorial properties are well behaved under…
We consider solvable matrix models. We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one…
Departing from a class of infinite series with central binomial coefficients in the numerator and depending on a positive integer parameter, we first extend known identities to all complex parameters. Then we use various methods, including…
This is an introduction to linear algebra and group theory. We first review the linear algebra basics, namely the determinant, the diagonalization procedure and more, and with the determinant being constructed as it should, as a signed…
Orthogonal - unitary and symplectic - unitary crossover ensembles of random matrices are relevant in many contexts, especially in the study of time reversal symmetry breaking in quantum chaotic systems. Using skew-orthogonal polynomials we…
The distribution of the characteristic polynomial $Z(U,\theta)$ of $N\times N$ matrices $U$ in the Circular Unitary Ensemble is studied by the method of second quantization for one-dimensional fermions. For infinite $N$ the Gaussian…
We have discussed earlier the correlation functions of the random variables $\det(\la-X)$ in which $X$ is a random matrix. In particular the moments of the distribution of these random variables are universal functions, when measured in the…
We show that character analysis using Fourier series is possible, at least when a mathematical character is considered. Previous approaches to character analysis are somewhat not in the spirit of harmonic analysis.
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
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…
Random number generators are widely used in practical algorithms. Examples include simulation, number theory (primality testing and integer factorization), fault tolerance, routing, cryptography, optimization by simulated annealing, and…
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…
Generalized additive models (GAMs) provide a way to blend parametric and non-parametric (function approximation) techniques together, making them flexible tools suitable for many modeling problems. For instance, GAMs can be used to…
We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary…
In this letter we generalise Ensemble Kalman inversion techniques to general Bayesian models where previously they were restricted to additive Gaussian likelihoods - all in the difficult setting where the likelihood can be sampled from, but…
A Moutard type transformation for matrix generalized analytic functions is derived. Relations between Moutard type transforms and gauge transformations are demonstrated.
In order to have a better understanding of finite random matrices with non-Gaussian entries, we study the $1/N$ expansion of local eigenvalue statistics in both the bulk and at the hard edge of the spectrum of random matrices. This gives…
This paper studies the unitary diagonalization of matrices over formal power series rings. Our main result shows that a normal matrix is unitarily diagonalizable if and only if its minimal polynomial completely splits over the ring and the…
We describe a generalization of the concept of a pc presentation that applies to groups with a nontrivial solvable radical. Such a representation can be much more efficient in terms of memory use and even of arithmetic, than permuattion and…
We propose a new modeling approach that is a generalization of generative and discriminative models. The core idea is to use an implicit parameterization of a joint probability distribution by specifying only the conditional distributions.…