Riemann Hilbert problem for bi-orthogonal polynomials
نویسندگان
چکیده
منابع مشابه
A Riemann-hilbert Problem for Skew-orthogonal Polynomials
Abstract. We find a local (d + 1)× (d + 1) Riemann-Hilbert problem characterizing the skew-orthogonal polynomials associated to the partition function of the Gaussian Orthogonal Ensemble of random matrices with a potential function of degree d. Our Riemann-Hilbert problem is similar to a local d × d RiemannHilbert problem found by Kuijlaars and McLaughlin characterizing the bi-orthogonal polyno...
متن کاملA Riemann-Hilbert problem for biorthogonal polynomials
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, Kapaev, and Bertola et al. We believe that our formulation may be tractable to asymptotic analysis.
متن کاملRiemann-hilbert Methods in the Theory of Orthogonal Polynomials
In this paper we describe various applications of the RiemannHilbert method to the theory of orthogonal polynomials on the line and on the circle.
متن کاملGeneralized orthogonal polynomials, discrete KP and Riemann-Hilbert problems
Classically, a single weight on an interval of the real line leads to moments, orthogonal polynomials and tridiagonal matrices. Appropriately deforming this weight with times t = (t1, t2, ...), leads to the standard Toda lattice and τ -functions, expressed as Hermitian matrix integrals. This paper is concerned with a sequence of t-perturbed weights, rather than one single weight. This sequence ...
متن کاملOrthogonal trigonometric polynomials: Riemann-Hilbert analysis and relations with OPUC
Abstract. In this paper, we study the theory of orthogonal trigonometric polynomials (OTP). We obtain asymptotics of OTP with positive and analytic weight functions by Riemann-Hilbert approach and find they have relations with orthogonal polynomials on the unit circle (OPUC). By the relations and the theory of OPUC, we also get four-terms recurrent formulae, ChristoffelDarboux formula and some ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2003
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/36/16/312