Determinantal Structure and Bulk Universality of Conditional Overlaps in the Complex Ginibre Ensemble

Akemann G, Tribe R, Tsareas A, Zaboronski O (2020)
Acta Physica Polonica B 51(7): 1611-1626.

Konferenzbeitrag | Veröffentlicht | Englisch
 
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Autor*in
Akemann, GernotUniBi; Tribe, Roger; Tsareas, Athanasios; Zaboronski, Oleg
Abstract / Bemerkung
In these proceedings, we summarise how the determinantal structure for the conditional overlaps among left and right eigenvectors emerges in the complex Ginibre ensemble at finite matrix size. An emphasis is put on the underlying structure of orthogonal polynomials in the complex plane and its analogy to the determinantal structure of k-point complex eigenvalue correlation functions. The off-diagonal overlap is shown to follow from the diagonal overlap conditioned on k >= 2 complex eigenvalues. As a new result, we present the local bulk scaling limit of the conditional overlaps away from the origin. It is shown to agree with the limit at the origin and is thus universal within this ensemble.
Erscheinungsjahr
2020
Band
51
Ausgabe
7
Seite(n)
1611-1626
Konferenz
Conference on Random Matrix Theory - Application in the Information Era
Konferenzort
Krakow, POLAND
ISSN
0587-4254
eISSN
1509-5770
Page URI
https://pub.uni-bielefeld.de/record/2945847

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Akemann G, Tribe R, Tsareas A, Zaboronski O. Determinantal Structure and Bulk Universality of Conditional Overlaps in the Complex Ginibre Ensemble. Acta Physica Polonica B . 2020;51(7):1611-1626.
Akemann, G., Tribe, R., Tsareas, A., & Zaboronski, O. (2020). Determinantal Structure and Bulk Universality of Conditional Overlaps in the Complex Ginibre Ensemble. Acta Physica Polonica B , 51(7), 1611-1626. doi:10.5506/APhysPolB.51.1611
Akemann, G., Tribe, R., Tsareas, A., and Zaboronski, O. (2020). Determinantal Structure and Bulk Universality of Conditional Overlaps in the Complex Ginibre Ensemble. Acta Physica Polonica B 51, 1611-1626.
Akemann, G., et al., 2020. Determinantal Structure and Bulk Universality of Conditional Overlaps in the Complex Ginibre Ensemble. Acta Physica Polonica B , 51(7), p 1611-1626.
G. Akemann, et al., “Determinantal Structure and Bulk Universality of Conditional Overlaps in the Complex Ginibre Ensemble”, Acta Physica Polonica B , vol. 51, 2020, pp. 1611-1626.
Akemann, G., Tribe, R., Tsareas, A., Zaboronski, O.: Determinantal Structure and Bulk Universality of Conditional Overlaps in the Complex Ginibre Ensemble. Acta Physica Polonica B . 51, 1611-1626 (2020).
Akemann, Gernot, Tribe, Roger, Tsareas, Athanasios, and Zaboronski, Oleg. “Determinantal Structure and Bulk Universality of Conditional Overlaps in the Complex Ginibre Ensemble”. Acta Physica Polonica B 51.7 (2020): 1611-1626.

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arXiv: 1912.09339

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