Related papers: Generalized Christoffel-Darboux formula for skew-o…
We give explicit upper bounds for coefficients of polynomials appearing in Gauss-Kra\"{i}tchik formula for cyclotomic polynomials. We use a certain relation between elementary symmetric polynomials and power sums polynomials.
A reduction procedure for stochastic differential equations based on stochastic symmetries including Girsanov random transformations is proposed. In this setting, a new notion of reconstruction is given, involving the expectation values of…
The Knop-Sahi interpolation Macdonald polynomials are inhomogeneous and nonsymmetric generalisations of the well-known Macdonald polynomials. In this paper we apply the interpolation Macdonald polynomials to study a new type of basic…
Gaussian elimination with partial pivoting (GEPP) is a widely used method to solve dense linear systems. Each GEPP step uses a row transposition pivot movement if needed to ensure the leading pivot entry is maximal in magnitude for the…
An important application of Lebesgue integral quadrature arXiv:1807.06007 is developed. Given two random processes, $f(x)$ and $g(x)$, two generalized eigenvalue problems can be formulated and solved. In addition to obtaining two Lebesgue…
Complementary Romanovski-Routh polynomials play an important role in extracting specific properties of orthogonal polynomials. In this work, a generalized form of the Complementary Romanovski-Routh polynomials (GCRR) that has the Gaussian…
In this work, we propose a new approach called ``stationary reduction method based on nonisospectral deformation of orthogonal polynomials" for deriving discrete Painlev\'{e}-type (d-P-type) equations. We apply this approach to…
Generalized Polynomial Chaos (gPC) expansions are well established for forward uncertainty propagation in many application areas. Although the associated computational effort may be reduced in comparison to Monte Carlo techniques, for…
We calculate the expectation value of an arbitrary product of characteristic polynomials of complex random matrices and their hermitian conjugates. Using the technique of orthogonal polynomials in the complex plane our result can be written…
This paper introduces a new generalized polynomial chaos expansion (PCE) comprising multivariate Hermite orthogonal polynomials in dependent Gaussian random variables. The second-moment properties of Hermite polynomials reveal a weakly…
We extend results of Zeitouni-Zelditch on large deviations principles for zeros of Gaussian random polynomials $s$ in one complex variable to certain non-Gaussian ensembles that we call $P(\phi)_2$ random polynomials. The probability…
The skew Schur functions admit many determinantal expressions. Chief among them are the (dual) Jacobi-Trudi formula and the Lascoux-Pragacz formula, which is a skew analogue of the Giambelli identity. Comparatively, the skew characters of…
We define in the framework of light-cone collinear factorization method, the chiral-odd generalized parton distributions (GPDs) of a pseudoscalar hadron (such as the $\pi^0$) up to twist 6. For that, we introduce the relevant matrix…
We present an exact sampling algorithm for Pfaffian point processes based on a skew-symmetric analogue of the Cholesky factorization. This algorithm enables efficient sampling of a wide range of statistics arising in random matrix theory…
In this paper, we present a new type of generating function of generalized Apostol-Bernoulli poly Daehee polynomial (GABPDP). By using the generating function of GABPDP, we discuss some special cases and useful identities of generalized…
In this paper, a higher order finite difference scheme is proposed for Generalized Fractional Diffusion Equations (GFDEs). The fractional diffusion equation is considered in terms of the generalized fractional derivatives (GFDs) which uses…
The generalisation of continuous orthogonal polynomial ensembles from random matrix theory to the $q$-lattice setting is considered. We take up the task of initiating a systematic study of the corresponding moments of the density from two…
We present an intriguing discovery related to Random Fourier Features: in Gaussian kernel approximation, replacing the random Gaussian matrix by a properly scaled random orthogonal matrix significantly decreases kernel approximation error.…
Recently, the use of Polynomial Chaos Expansion (PCE) has been increasing to study the uncertainty in mathematical models for a wide range of applications and several extensions of the original PCE technique have been developed to deal with…
We introduce the order-separated Grassmann higher-order tensor renormalization group (OS-GHOTRG) method for QCD with staggered quarks in the strong-coupling expansion. The method allows us to determine the expansion coefficients of the…