scholarly journals Differential Systems for Biorthogonal Polynomials Appearing in 2-Matrix Models and the Associated Riemann?Hilbert Problem

2003 ◽  
Vol 243 (2) ◽  
pp. 193-240 ◽  
Author(s):  
M. Bertola ◽  
B. Eynard ◽  
J. Harnad
Keyword(s):  
Matrix Models ◽  
Hilbert Problem ◽  
Differential Systems ◽  
Biorthogonal Polynomials ◽  
Riemann Hilbert Problem

Large N-limit for random matrices with external source with three distinct eigenvalues

2016 ◽  
Vol 05 (02) ◽  
pp. 1650005
Author(s):  
Jian Xu ◽  
Engui Fan ◽  
Yang Chen
Keyword(s):  
Matrix Models ◽  
Random Matrices ◽  
Random Matrix ◽  
Hilbert Problem ◽  
External Source ◽  
Universal Behavior ◽  
Large N ◽  
Random Matrix Models ◽  
Riemann Hilbert Problem ◽  
Sine Kernel

In this paper, we analyze the large N-limit for random matrix with external source with three distinct eigenvalues. And we confine ourselves in the Hermite case and the three distinct eigenvalues are [Formula: see text]. For the case [Formula: see text], we establish the universal behavior of local eigenvalue correlations in the limit [Formula: see text], which is known from unitarily invariant random matrix models. Thus, local eigenvalue correlations are expressed in terms of the sine kernel in the bulk and in terms of the Airy kernel at the edge of the spectrum. The result can be obtained by analyzing [Formula: see text] Riemann–Hilbert problem via nonlinear steepest decent method.

scholarly journals A Riemann–Hilbert problem for biorthogonal polynomials

2005 ◽  
Vol 178 (1-2) ◽  
pp. 313-320 ◽  
Author(s):  
A.B.J. Kuijlaars ◽  
K.T.-R. McLaughlin
Keyword(s):  
Hilbert Problem ◽  
Biorthogonal Polynomials ◽  
Riemann Hilbert Problem

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

scholarly journals Isomonodromy Aspects of the tt* Equations of Cecotti and Vafa II: Riemann–Hilbert Problem

2015 ◽  
Vol 336 (1) ◽  
pp. 337-380 ◽  
Author(s):  
Martin A. Guest ◽  
Alexander R. Its ◽  
Chang-Shou Lin
Keyword(s):  
Hilbert Problem ◽  
Riemann Hilbert Problem

scholarly journals The Riemann–Hilbert problem and the generalized Neumann kernel

2005 ◽  
Vol 182 (2) ◽  
pp. 388-415 ◽  
Author(s):  
R. Wegmann ◽  
A.H.M. Murid ◽  
M.M.S. Nasser
Keyword(s):  
Hilbert Problem ◽  
Generalized Neumann Kernel ◽  
Neumann Kernel ◽  
Riemann Hilbert Problem
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