Related papers: Biorthogonal ensembles with two-particle interacti…
We consider the biorthogonal polynomials associated to the two-matrix model where the eigenvalue distribution has potentials V_1,V_2 with arbitrary rational derivative and whose supports are constrained on an arbitrary union of intervals…
In this paper, we consider Muttalib-Borodin ensemble of Laguerre type, a determinantal point process over $[0,\infty)$ which depends on the varying weights $x^{\alpha}e^{-nV(x)}$, $\alpha>-1$, and a parameter $\theta$. For $\theta$ being a…
We characterize the biorthogonal polynomials that appear in the theory of coupled random matrices via a Riemann-Hilbert problem. Our Riemann-Hilbert problem is different from the ones that were proposed recently by Ercolani and McLaughlin,…
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…
The Muttalib-Borodin biorthogonal ensemble is a probability density function for $n$ particles on the positive real line that depends on a parameter $\theta$ and an external field $V$. For $\theta=\frac{1}{2}$ we find the large $n$ behavior…
We consider the Plancherel-Rotach type asymptotics of the biorthogonal polynomials associated to the biorthogonal ensemble with the joint probability density function \begin{equation*} \frac{1}{C} \prod_{1 \leq i < j \leq n} (\lambda_j…
We consider biorthogonal polynomials that arise in the study of a generalization of two--matrix Hermitian models with two polynomial potentials V_1(x), V_2(y) of any degree, with arbitrary complex coefficients. Finite consecutive…
We prove the edge and bulk universality of random Hermitian matrices with equi-spaced external source. One feature of our method is that we use neither a Christoffel-Darboux type formula, nor a double-contour formula, which are standard…
We study the singular values of the product of two coupled rectangular random matrices as a determinantal point process. Each of the two factors is given by a parameter dependent linear combination of two independent, complex Gaussian…
The paper investigates the properties of certain biorthogonal polynomials appearing in a specific simultaneous Hermite-Pade' approximation scheme. Associated to any totally positive kernel and a pair of positive measures on the positive…
Let $E = \cup_{j = 1}^l [a_{2j-1},a_{2j}],$ $a_1 < a_2 < ... < a_{2l},$ $l \geq 2$ and set ${\boldmath$\omega$}(\infty) =(\omega_1(\infty),...,\omega_{l-1}(\infty))$, where $\omega_j(\infty)$ is the harmonic measure of $[a_{2 j - 1}, a_{2…
We consider ensembles of random matrices, known as biorthogonal ensembles, whose eigenvalue probability density function can be written as a product of two determinants. These systems are closely related to multiple orthogonal functions. It…
In recent years, there has been significant progress in the theory of orthogonal polynomials on algebraic curves, particularly on genus 1 surfaces. In this paper, we focus on elliptic orthogonal polynomials and establish several of their…
We consider four nontrivial ensembles involving Gaussian Wigner and Wishart matrices. These are relevant to problems ranging from multiantenna communication to random supergravity. We derive the matrix probability density, as well as the…
We consider the two sequences of biorthogonal polynomials (p_{k,n})_k and (q_{k,n})_k related to the Hermitian two-matrix model with potentials V(x) = x^2/2 and W(y) = y^4/4 + ty^2. From an asymptotic analysis of the coefficients in the…
We distinguish a class of random point processes which we call Giambelli compatible point processes. Our definition was partly inspired by determinantal identities for averages of products and ratios of characteristic polynomials for random…
The statistical distribution of eigenvalues of pairs of coupled random matrices can be expressed in terms of integral kernels having a generalized Christoffel--Darboux form constructed from sequences of biorthogonal polynomials. For…
We construct biorthogonal polynomials for a measure over the complex plane which consists in the exponential of a potential V(z,z*) and in a set of external sources at the numerator and at the denominator. We use the pseudonorm of these…
We consider the class of biorthogonal polynomials that are used to solve the inverse spectral problem associated to elementary co-adjoint orbits of the Borel group of upper triangular matrices; these orbits are the phase space of…
We study orthogonal polynomials with periodically modulated Jacobi parameters in the case when $0$ lies on the soft edge of the spectrum of the corresponding periodic Jacobi matrix. We determine when the orthogonality measure is absolutely…