scholarly journals LARGE N ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS FROM INTEGRABILITY TO ALGEBRAIC GEOMETRY

2006 ◽  
pp. 489-513 ◽  
Author(s):  
B. Eynard
Keyword(s):  
Algebraic Geometry ◽  
Orthogonal Polynomials ◽  
Large N ◽  
Asymptotics Of Orthogonal Polynomials

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 Asymptotics of orthogonal polynomials beyond the scope of Szegő’s theorem

2006 ◽  
Vol 40 (4) ◽  
pp. 264-272
Author(s):  
F. Peherstorfer ◽  
A. Volberg ◽  
P. Yuditskii
Keyword(s):  
Orthogonal Polynomials ◽  
Asymptotics Of Orthogonal Polynomials
Sign in / Sign up

Export Citation Format

Share Document