相关论文: Perturbed Hankel Determinants

Motivated by recent results in random matrix theory we will study the distributions arising from products of complex Gaussian random matrices and truncations of Haar distributed unitary matrices. We introduce an appropriately general class…

We consider the five-vertex model on a finite square lattice with fixed boundary conditions such that the configurations of the model are in a one-to-one correspondence with the boxed plane partitions (3D Young diagrams which fit into a box…

Nonlinear statistics (i.e. statistics of permanents) on the eigenvalues of invariant random matrix models are considered for the three Dyson's symmetry classes $\beta=1,2,4$. General formulas in terms of hyperdeterminants are found for…

Applying the Jacobi method of second variation to the Bianchi IX system in Misner variables $(\alpha, \beta_+, \beta_-)$, we specialize to the Taub space background $(\beta_- = 0)$ and obtain the governing equations for linearized…

Let $f$ be analutic in the unit disk $\mathbb D$ and normalized so that $f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper we give sharp bound of Hankel determinant of the second order for the class of analytic unctions satisfying \[ \left|\arg…

Willems' fundamental lemma enables a trajectory-based characterization of linear systems through data-based Hankel matrices. However, in the presence of measurement noise, we ask: Is this noisy Hankel-based model expressive enough to…

Previous works have considered the leading correction term to the scaled limit of various correlation functions and distributions for classical random matrix ensembles and their $\beta$ generalisations at the hard and soft edge. It has been…

We characterize Fredholm determinants of a class of Hankel composition operators via matrix-valued Riemann-Hilbert problems, for additive and multiplicative compositions. The scalar-valued kernels of the underlying integral operators are…

We prove two inequalities regarding the ratio $\det(A+D)/\det A$ of the determinant of a positive-definite matrix $A$ and the determinant of its perturbation $A+D$. In the first problem, we study the perturbations that happen when positive…

In this work, we construct a stable and fairly fast estimator for solving non-parametric multidimensional regression problems. The proposed estimator is based on the use of multivariate Jacobi polynomials that generate a basis for a reduced…

We determine the probability that a random n x n symmetric matrix over {1, 2, ... , m} has determinant divisible by m.

We study asymptotics of the recurrence coefficients of orthogonal polynomials associated to the generalized Jacobi weight, which is a weight function with a finite number of algebraic singularities on $[-1,1]$. The recurrence coefficients…

The eigenvalue correlations of random matrices from the Jacobi Unitary Ensemble have a known asymptotic behavior as their size tends to infinity. In the bulk of the spectrum the behavior is described in terms of the sine kernel, and at the…

In this paper we commence the study of discrete harmonic analysis associated with Jacobi orthogonal polynomials of order $(\alpha,\beta)$. Particularly, we give the solution $W^{(\alpha,\beta)}_t$, $t\ge 0$, and some properties of the heat…

Using continued fraction expansions of certain polygamma functions as a main tool, we find orthogonal polynomials with respect to the odd-index Bernoulli polynomials $B_{2k+1}(x)$ and the Euler polynomials $E_{2k+\nu}(x)$, for $\nu=0, 1,…

We obtain large $N$ asymptotics for $N \times N$ Hankel determinants corresponding to non-negative symbols with Fisher-Hartwig (FH) singularities in the multi-cut regime. Our result includes the explicit computation of the multiplicative…

We present a formula that expresses the Hankel determinants of a linear combination of length $d+1$ of moments of orthogonal polynomials in terms of a $d\times d$ determinant of the orthogonal polynomials. This formula exists somehow hidden…

We study a sequence of polynomials orthogonal with respect to a one parameter family of weights $$ w(x):=w(x,t)=\rex^{-t/x}\:x^{\al}(1-x)^{\bt},\quad t\geq 0, $$ defined for $x\in[0,1].$ If $t=0,$ this reduces to a shifted Jacobi weight.…

A one-variable Hankel matrix $H_a$ is an infinite matrix $H_a=[a(i+j)]_{i,j\geq0}$. Similarly, for any $d\geq2$, a $d$-variable Hankel matrix is defined as $H_{\mathbf{a}}=[\mathbf{a}(\mathbf{i}+\mathbf{j})]$, where…

In a recent work Killip and Nenciu gave random recurrences for the characteristic polynomials of certain unitary and real orthogonal upper Hessenberg matrices. The corresponding eigenvalue p.d.f.'s are beta-generalizations of the classical…