Related papers: A 3D Ginibre point field

Tracy and Widom showed that fundamentally important kernels in random matrix theory arise from differential equations with rational coefficients. More generally, this paper considers symmetric Hamiltonian systems abd determines the…

One object of interest in random matrix theory is a family of point ensembles (random point configurations) related to various systems of classical orthogonal polynomials. The paper deals with a one--parametric deformation of these…

We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…

In this paper, we give some results on closed polynomials and factorially closed polynomial in $n$ variables. In particular, we give a characterization of factorially closed polynomials in $n$ variables over an algebraically closed field…

In this paper, we present some applications of quaternions and octonions. We present the real matrix representations for complex octonions and some of their properties which can be used in computations where these elements are involved.…

We introduce the notion of "quasi-symmetric" polynomials, which is a generalization of the notion of symmetry, and is particularly suited to the setting of polynomial rings over finite fields. The properties of this new class of functions…

Polynomial ensembles are determinantal point processes associated with (non necessarily orthogonal) projections onto polynomial subspaces. The aim of this survey article is to put forward the use of recurrence coefficients to obtain the…

The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…

We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a $N\times N$ random matrix taken from a $L$-deformed Chiral Gaussian Unitary Ensemble with an…

We analyze the Nystr\"om approximation of a positive definite kernel associated with a probability measure. We first prove an improved error bound for the conventional Nystr\"om approximation with i.i.d. sampling and singular-value…

More analysis of operator determinants on homogeneous three dimensional lens spaces is presented with the emphasis on numerics so that Laplacians for massive fields can be dealt with. Polyhedral quotients are also briefly considered.…

For orthogonal polynomials defined by compact Jacobi matrix with exponential decay of the coefficients, precise properties of orthogonality measure is determined. This allows showing uniform boundedness of partial sums of orthogonal…

In this paper we describe an intrinsically geometric way of producing magnetic fields on $\S^3$ and $\R^3$ for which the corresponding Dirac operators have a non-trivial kernel. In many cases we are able to compute the dimension of the…

The partly symmetric real Ginibre ensemble consists of matrices formed as linear combinations of real symmetric and real anti-symmetric Gaussian random matrices. Such matrices typically have both real and complex eigenvalues. For a fixed…

Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon satisfying simple geometric criteria, our construction produces 2n…

We study a reproducing kernel Hilbert space of functions defined on the positive integers and associated to the binomial coefficients. We introduce two transforms, which allow us to develop a related harmonic analysis in this Hilbert space.…

The main goal of this paper is to extend [J. Algebra Appl. 20 (2021), 2150074] to generalized quaternion algebras, even when these algebras are not necessarily division rings. More precisely, in such cases, the image of a multilinear…

For the bi-orthogonal polynomials with the third degree polynomial potential functions, the 3 x 3 matrix Riemann-Hilbert problem is explicitly constructed. The developed approach admits an extension to the bi-orthogonal polynomials with…

In this note, we provide explicit expressions for the projections onto the graph of a quadratic polynomial. The projections are obtained by examining the critical points of the associated quartic polynomial, that is, the roots of the cubic…