scholarly journals Painlevé transcendents and the Hankel determinants generated by a discontinuous Gaussian weight

2018 ◽  
Vol 42 (1) ◽  
pp. 301-321 ◽  
Author(s):  
Chao Min ◽  
Yang Chen
Keyword(s):  
Hankel Determinants ◽  
Painlevé Transcendents ◽  
Painleve Transcendents ◽  
Gaussian Weight

The meromorphic nature of the sixth Painlevé transcendents

2004 ◽  
Vol 94 (1) ◽  
pp. 319-342 ◽  
Author(s):  
Aimo Hinkkanen ◽  
Ilpo Laine
Keyword(s):  
Painlevé Transcendents ◽  
Painleve Transcendents

Meromorphic Painlevé transcendents at a fixed singularity

2013 ◽  
Vol 286 (8-9) ◽  
pp. 861-875 ◽  
Author(s):  
Kazuo Kaneko ◽  
Yousuke Ohyama
Keyword(s):  
Painlevé Transcendents ◽  
Fixed Singularity ◽  
Painleve Transcendents

scholarly journals Asymptotics of Hankel Determinants With a One-Cut Regular Potential and Fisher–Hartwig Singularities

2018 ◽  
Vol 2019 (24) ◽  
pp. 7515-7576 ◽  
Author(s):  
Christophe Charlier
Keyword(s):  
Point Process ◽  
Characteristic Polynomial ◽  
Hermitian Matrix ◽  
Piecewise Constant ◽  
Hankel Determinants ◽  
Type Singularity ◽  
Gap Probability ◽  
Gaussian Weight

Abstract We obtain asymptotics of large Hankel determinants whose weight depends on a one-cut regular potential and any number of Fisher–Hartwig singularities. This generalises two results: (1) a result of Berestycki, Webb, and Wong [5] for root-type singularities and (2) a result of Its and Krasovsky [37] for a Gaussian weight with a single jump-type singularity. We show that when we apply a piecewise constant thinning on the eigenvalues of a random Hermitian matrix drawn from a one-cut regular ensemble, the gap probability in the thinned spectrum, as well as correlations of the characteristic polynomial of the associated conditional point process, can be expressed in terms of these determinants.

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