## 53 Citations

### Strong asymptotics for Cauchy biorthogonal polynomials

- Mathematics
- 2012

where U, V are scalar functions defined on R. The model was termed the Cauchy matrix model because of the shape of the coupling term. Similarly to the case of the Hermitean one-matrix models for…

### Hermite-Padé approximation and integrability

- MathematicsArXiv
- 2022

The result explains the appearence of various ingredients of the integrable systems theory in application to multiple orthogonal polynomials, numerical algorthms, random matrices, and in other branches of mathematical physics and applied mathematics where the Hermite–Padé approximation problem is relevant.

### Cauchy–Laguerre Two-Matrix Model and the Meijer-G Random Point Field

- Mathematics
- 2014

We apply the general theory of Cauchy biorthogonal polynomials developed in Bertola et al. (Commun Math Phys 287(3):983–1014, 2009) and Bertola et al. (J Approx Th 162(4):832–867, 2010) to the case…

### Cauchy–Laguerre Two-Matrix Model and the Meijer-G Random Point Field

- MathematicsCommunications in Mathematical Physics
- 2013

We apply the general theory of Cauchy biorthogonal polynomials developed in Bertola et al. (Commun Math Phys 287(3):983–1014, 2009) and Bertola et al. (J Approx Th 162(4):832–867, 2010) to the case…

### Hermite-Padé approximations with Pfaffian structures: Novikov peakon equation and integrable lattices

- MathematicsAdvances in Mathematics
- 2022

### On matrix Cauchy biorthogonal polynomials

- MathematicsIntegral Transforms and Special Functions
- 2021

In this paper, we study the sequences of matrix Cauchy biorthogonal polynomials. We will focus on the algebraic aspects of the problem, finding a connection with a kind of matrix mixed-type…

### Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model

- Mathematics
- 2013

We apply the nonlinear steepest descent method to a class of 3 × 3 Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix random model. The general case of two equilibrium…

### Strong asymptotic of Cauchy biorthogonal polynomials and orthogonal polynomials with varying measure

- Mathematics
- 2021

. We give the strong asymptotic of Cauchy biorthogonal polynomials under the assumption that the deﬁning measures are supported on bounded non intersecting intervals of the real line and satisfy…

### Some biorthogonal polynomials arising in numerical analysis and approximation theory

- MathematicsJournal of Computational and Applied Mathematics
- 2022

### Gap probabilities for the Bures-Hall Ensemble and the Cauchy-Laguerre Two-Matrix Model

- Mathematics
- 2022

Abstract. The Bures metric and the associated Bures-Hall measure is arguably the best choice for studying the spectrum of the quantum mechanical density matrix with no apriori knowledge of the…

## References

SHOWING 1-10 OF 50 REFERENCES

### Biorthogonal polynomials for two-matrix models with semiclassical potentials

- MathematicsJ. Approx. Theory
- 2007

### Asymptotics and integrable structures for biorthogonal polynomials associated to a random two-matrix model

- Mathematics
- 2001

### Duality, Biorthogonal Polynomials¶and Multi-Matrix Models

- Mathematics
- 2002

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…

### Differential Systems for Biorthogonal Polynomials Appearing in 2-Matrix Models and the Associated Riemann–Hilbert Problem

- Mathematics
- 2003

AbstractWe consider biorthogonal polynomials that arise in the study of a generalization of two–matrix Hermitian models with two polynomial potentials V1(x), V2(y) of any degree, with arbitrary…

### Cubic string boundary value problems and Cauchy biorthogonal polynomials

- Mathematics
- 2009

Cauchy biorthogonal polynomials appear in the study of special solutions to the dispersive nonlinear partial differential equation called the Degasperis–Procesi (DP) equation, as well as in certain…

### Strong asymptotics for Cauchy biorthogonal polynomials

- Mathematics
- 2012

where U, V are scalar functions defined on R. The model was termed the Cauchy matrix model because of the shape of the coupling term. Similarly to the case of the Hermitean one-matrix models for…

### The Cauchy Two-Matrix Model

- Mathematics
- 2008

We introduce a new class of two(multi)-matrix models of positive Hermitian matrices coupled in a chain; the coupling is related to the Cauchy kernel and differs from the exponential coupling more…

### Riemann-Hilbert Problems for Multiple Orthogonal Polynomials

- Mathematics
- 2001

In the early nineties, Fokas, Its and Kitaev observed that there is a natural Riemann-Hilbert problem (for 2 x×2 matrix functions) associated with a system of orthogonal polynomials. This…

### Degasperis-Procesi peakons and the discrete cubic string

- Mathematics
- 2005

We use an inverse scattering approach to study multi-peakon solutions of the Degasperis–Procesi (DP) equation, an integrable PDE similar to the Camassa–Holm shallow water equation. The spectral…

### Moment determinants as isomonodromic tau functions

- Mathematics
- 2008

We consider a wide class of determinants whose entries are moments of the so-called semiclassical functionals and we show that they are tau functions for an appropriate isomonodromic family which…