Toeplitz Determinants: Some Applications, Theorems, and Conjectures

2007 ◽  
pp. 333-353 ◽  
Author(s):  
Michael E. Fisher ◽  
Robert E. Hartwig
Keyword(s):  
Toeplitz Determinants

scholarly journals Multiple phases in a generalized Gross-Witten-Wadia matrix model

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Jorge G. Russo ◽  
Miguel Tierz
Keyword(s):  
Partition Function ◽  
Matrix Models ◽  
Characteristic Polynomial ◽  
Matrix Model ◽  
Phase Structure ◽  
Unitary Matrix ◽  
Two Dimensional ◽  
Toeplitz Determinants ◽  
Dimensional Parameter ◽  
Planar Limit

Abstract We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large N results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large N (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

scholarly journals Emergence of a singularity for Toeplitz determinants and Painlevé V

2011 ◽  
Vol 160 (2) ◽  
pp. 207-262 ◽  
Author(s):  
T. Claeys ◽  
A. Its ◽  
I. Krasovsky
Keyword(s):  
Toeplitz Determinants
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