Related papers: Mixed Correlation Functions of the Two-Matrix Mode…
We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…
We study the problem of merging sequential or independent e-values into one e-value or e-process. We describe a class of e-value merging functions via martingales and show that it dominates all merging methods for sequential e-values. All…
We investigate correlation functions in a periodic box-ball system. For the second and the third nearest neighbor correlation functions, we give explicit formulae obtained by combinatorial methods. A recursion formula for a specific…
In this contribution we introduce a mixed interpolation-regression operator for functions defined in some domains of the plane. We focus the attention on the ellipse, an annulus and a polygon. An upper bound for such an operator is…
Calculating the values of nuclear correlation functions is computationally intensive due to the fact that the number of terms in a nuclear wave function scales exponentially with atomic number. To speed up this computation, we represent a…
Given a description of the stacking statistics of layered close-packed structures in the form of a hidden Markov model, we develop analytical expressions for the pairwise correlation functions between the layers. These may be calculated…
In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized…
This paper develops a polynomial normal transformation model, whereby various non-normal probability distributions can be simulated by the standard normal distribution. Two methods are presented to determine the coefficients of polynomial…
We apply matrix methods to arithmetic functions by associating matrices to the functions in a manner drawn from the theory of symmetric functions. Then we study the characteristic polynomials of the associated matrices.
We study correlation functions of the characteristic polynomials in coupled matrix models based on the Schur polynomial expansion, which manifests their determinantal structure.
For one-matrix models with polynomial potentials, the explicit relationship between the partition function and the isomonodromic tau function for the 2x2 polynomial differential systems satisfied by the associated orthogonal polynomials is…
A polynomial triangle is an array whose inputs are the coefficients in integral powers of a polynomial. Although polynomial coefficients have appeared in several works, there is no systematic treatise on this topic. In this paper we plan to…
In this work is presented a study on matrix biorthogonal polynomials sequences that satisfy a nonsymmetric recurrence relation with unbounded coefficients. The ratio asymptotic for this family of matrix biorthogonal polynomials is derived…
We derive conditions under which alternating renewal processes can be used to construct correlated Poisson processes. The pairwise correlation function is also derived, showing that the resulting correlations can be negative. The technique…
Consider the product of $M$ quadratic random matrices with complex elements and no further symmetry, where all matrix elements of each factor have a Gaussian distribution. This generalises the classical Wishart-Laguerre Gaussian Unitary…
We construct rational all-pass matrix functions with real-valued coefficients for mirroring pairs of complex-conjugated determinantal roots of a rational matrix. This problem appears, for example, when proving the spectral factorization…
We consider matrix orthogonal polynomials related to Bessel type matrices of weights that can be defined in terms of a given matrix Pearson equation. From a Riemann-Hilbert problem we derive first and second order differential relations for…
We have found an exact formula expressing a general correlation function containing both products and ratios of characteristic polynomials of random Hermitian matrices. The answer is given in the form of a determinant. An essential…
We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients between two sets of orthonormal polynomials, another example…
There are two kinds of polynomial functions on matrix algebras over commutative rings: those induced by polynomials with coefficients in the algebra itself and those induced by polynomials with scalar coefficients. In the case of algebras…