In this work we consider the extension of the one variable Bernstein–Szegő theory for orthogonal polynomials on the real line (see [3]) to bivariate measures supported on the triangle. A similar problem for measures supported in the square was studied in [1]. Following essentially [2] the orthogonal polynomials and the corresponding kernel functions are constructed. Finally, some asymptotic res...

Bleher and Kuijlaars recently showed that the eigenvalue correlations from matrix ensembles with external source can be expressed by means of a kernel built out of special multiple orthogonal polynomials. We derive a Christoffel-Darboux formula for this kernel for general multiple orthogonal polynomials. In addition, we show that the formula can be written in terms of the solution of the Rieman...

We study a relation between Hadamard powers and polynomial kernel perceptrons. The rank of for the special case Boolean matrix generic real is computed explicitly. These results are interpreted in terms classification capacities

Given a complex manifold M endowed with a hermitian metric g and supporting a smooth probability measure μ, there is a naturally associated Dirichlet form operator A on L(μ). If b is a function in L(μ) there is a naturally associated Hankel operator Hb defined in holomorphic function spaces over M . We establish a relation between hypercontractivity properties of the semigroup e−tA and boundedn...

We study multivariable Christoffel–Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation functions for products of characteristic polynomials of random Hermitian matrices. Using their interpretation as reproducing kernels, we obtain simple proofs of Pfaffian and determinant formulas, as well as Schur polynomial expansions, ...

The microscopic correlation functions of non-chiral random matrix models with complex eigenvalues are analyzed for a wide class of non-Gaussian measures. In the large-N limit of weak non-Hermiticity, where N is the size of the complex matrices, we can prove that all k-point correlation functions including an arbitrary number of Dirac mass terms are universal close to the origin. To this aim we ...

The scientific and effective prediction of drawbar pull is of great importance in the evaluation of military vehicle trafficability. Nevertheless, the existing prediction models have demonstrated lots of inherent limitations. In this framework, a multiple-kernel relevance vector machine model (MkRVM) including Gaussian kernel and polynomial kernel is proposed to predict drawbar pull. Nonlinear ...

Exploring Complexity of Large Update Interior-Point Methods for ) k ( P* Linear Complementarity Problems Based on Kernel Function KEYVAN AMINI* M.REZA PEYGHAMI +,2 ∗ Department of Sciences, Razi University, Kermanshah, Iran + Department of Sciences, Khajeh Nasir Toosi (KNT) University of Technology, Tehran, Iran Abstract. Interior Point Methods not only are the most effective methods in practic...