scholarly journals Planar orthogonal polynomials and boundary universality in the random normal matrix model

2021 ◽  
Vol 227 (2) ◽  
pp. 309-406
Author(s):  
Håkan Hedenmalm ◽  
Aron Wennman
Keyword(s):  
Orthogonal Polynomials ◽  
Matrix Model ◽  
Normal Matrix

scholarly journals Orthogonal polynomials in the normal matrix model with a cubic potential

2012 ◽  
Vol 230 (3) ◽  
pp. 1272-1321 ◽  
Author(s):  
Pavel M. Bleher ◽  
Arno B.J. Kuijlaars
Keyword(s):  
Orthogonal Polynomials ◽  
Matrix Model ◽  
Normal Matrix

PHASE DIAGRAM AND ORTHOGONAL POLYNOMIALS IN MULTIPLE-WELL MATRIX MODELS

1991 ◽  
Vol 06 (25) ◽  
pp. 4491-4515 ◽  
Author(s):  
OLAF LECHTENFELD ◽  
RASHMI RAY ◽  
ARUP RAY
Keyword(s):  
Phase Diagram ◽  
Orthogonal Polynomials ◽  
Matrix Models ◽  
Matrix Model ◽  
Phase Structure ◽  
Saddle Points ◽  
Tree Level ◽  
Potential Wells ◽  
Large N

We investigate a zero-dimensional Hermitian one-matrix model in a triple-well potential. Its tree-level phase structure is analyzed semiclassically as well as in the framework of orthogonal polynomials. Some multiple-arc eigenvalue distributions in the first method correspond to quasiperiodic large-N behavior of recursion coefficients for the second. We further establish this connection between the two approaches by finding three-arc saddle points from orthogonal polynomials. The latter require a modification for nondegenerate potential minima; we propose weighing the average over potential wells.

scholarly journals Rescaling Ward Identities in the Random Normal Matrix Model

2018 ◽  
Vol 50 (1) ◽  
pp. 63-127 ◽  
Author(s):  
Yacin Ameur ◽  
Nam-Gyu Kang ◽  
Nikolai Makarov
Keyword(s):  
Matrix Model ◽  
Normal Matrix ◽  
Ward Identities

scholarly journals LARGE-N AND BETHE ANSATZ

2004 ◽  
Vol 19 (22) ◽  
pp. 1661-1667 ◽  
Author(s):  
BRANISLAV JURČO
Keyword(s):  
Saddle Point ◽  
Orthogonal Polynomials ◽  
Matrix Models ◽  
Bethe Ansatz ◽  
Integrable System ◽  
Matrix Model ◽  
Integrable Model ◽  
Saddle Point Approximation ◽  
Large N ◽  
The Matrix

We describe an integrable model, related to the Gaudin magnet, and its relation to the matrix model of Brézin, Itzykson, Parisi and Zuber. Relation is based on Bethe ansatz for the integrable model and its interpretation using orthogonal polynomials and saddle point approximation. Large-N limit of the matrix model corresponds to the thermodynamic limit of the integrable system. In this limit (functional) Bethe ansatz is the same as the generating function for correlators of the matrix models.

scholarly journals The supercritical regime in the normal matrix model with cubic potential

2015 ◽  
Vol 283 ◽  
pp. 530-587 ◽  
Author(s):  
A.B.J. Kuijlaars ◽  
A. Tovbis
Keyword(s):  
Matrix Model ◽  
Normal Matrix ◽  
Supercritical Regime

scholarly journals 2D string theory as normal matrix model

2003 ◽  
Vol 667 (1-2) ◽  
pp. 90-110 ◽  
Author(s):  
Sergei Yu. Alexandrov ◽  
Vladimir A. Kazakov ◽  
Ivan K. Kostov
Keyword(s):  
String Theory ◽  
Matrix Model ◽  
Normal Matrix
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