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Project C6: Coupled random matrices in field theory and statistical mechanics


Principal Investigator(s)
Gernot Akemann
Visitor(s)
Currently no visitors.

Summary:

In this project we study random matrices that are not independent. Emphasis will be put on coupled non-Hermitian matrices with complex eigenvalues, and their interpolation to the Hermitian limit. This topic has seen important developments in the past funding period, regarding analytical aspects, classification and applications in statistical mechanics and field theory. We aim at a deeper understanding of the related problem of two-dimensional static Coulomb gases in a confining potential at general temperatures, which generalizes the random matrix framework.


Recent Preprints:

26008 Gernot Akemann, Georg Angermann, Noah Aygün, Adam Mielke, Patricia Päßler, Christoph Raitzig, Tobias Winkler PDF

Three non-Hermitian random matrix universality classes of complex edge statistics: Spacing ratios and distributions

Project: C6

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Three non-Hermitian random matrix universality classes of complex edge statistics: Spacing ratios and distributions


Authors: Gernot Akemann, Georg Angermann, Noah Aygün, Adam Mielke, Patricia Päßler, Christoph Raitzig, Tobias Winkler Projects: C6
Submission Date: 10.04.2026 Submitter: Friedrich Götze
Download: PDF Link: 26008

26007 Gernot Akemann, Georg Angermann, Mario Kieburg, Adrian Padellaro PDF

Derivative relations for determinants, Pfaffians and characteristic polynomials in random matrix theory

Project: C6

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Derivative relations for determinants, Pfaffians and characteristic polynomials in random matrix theory


Authors: Gernot Akemann, Georg Angermann, Mario Kieburg, Adrian Padellaro Projects: C6
Submission Date: 10.04.2026 Submitter: Friedrich Götze
Download: PDF Link: 26007

25064 Gernot Akemann, Yan Fyodorov, Dmitry Savin PDF

Spectral Density and Eigenvector Nonorthogonality in Complex Symmetric Random Matrices

Project: C6

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Spectral Density and Eigenvector Nonorthogonality in Complex Symmetric Random Matrices


Authors: Gernot Akemann, Yan Fyodorov, Dmitry Savin Projects: C6
Submission Date: 01.12.2025 Submitter: Friedrich Götze
Download: PDF Link: 25064

25031 Gernot Akemann, Francesco Mezzadri, Patricia Päßler, Henry Taylor PDF

Logarithmic spectral distribution of a non-Hermitian $\beta$-ensemble

Project: C6

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Logarithmic spectral distribution of a non-Hermitian $\beta$-ensemble


Authors: Gernot Akemann, Francesco Mezzadri, Patricia Päßler, Henry Taylor Projects: C6
Submission Date: 28.04.2025 Submitter: Friedrich Götze
Download: PDF Link: 25031

25026 Adrian Padellaro, Sanjaye Ramgoolam, Rak-Kyeong Seong PDF

Row and column detection complexities of character tables

Project: A5, C6

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Row and column detection complexities of character tables


Authors: Adrian Padellaro, Sanjaye Ramgoolam, Rak-Kyeong Seong Projects: A5, C6
Submission Date: 14.03.2025 Submitter: Gernot Akemann
Download: PDF Link: 25026

24098 Gernot Akemann, Maurice Duits, Leslie Diëgo Molag PDF

Fluctuations in various regimes of non-hermiticity and a holographic principle

Project: C6

To appear: Annales Henri Poincare (2026)

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Fluctuations in various regimes of non-hermiticity and a holographic principle


Authors: Gernot Akemann, Maurice Duits, Leslie Diëgo Molag Projects: C6
Submission Date: 03.01.2025 Submitter: Friedrich Götze
Download: PDF Link: 24098
To appear: Annales Henri Poincare (2026)

24064 Gernot Akemann, Noah Aygün, Mario Kieburg, Patricia Päßler PDF

Complex symmetric, self-dual, and Ginibre random matrices: Analytical results for three classes of bulk and edge statistics

Project: C6

Published: Journal of Physics A: Mathematical and Theoretical 58, no. 12 (2025), 125204

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Complex symmetric, self-dual, and Ginibre random matrices: Analytical results for three classes of bulk and edge statistics


Authors: Gernot Akemann, Noah Aygün, Mario Kieburg, Patricia Päßler Projects: C6
Submission Date: 08.11.2024 Submitter: Friedrich Götze
Download: PDF Link: 24064
Published: Journal of Physics A: Mathematical and Theoretical 58, no. 12 (2025), 125204

24060 Adrian Padellaro, Sanjaye Ramgoolam, Ryo Suzuki PDF

Eigenvalue systems for integer orthogonal bases of multi-matrix invariants at finite $N$

Project: C6

Published: Journal of High Energy Physics 2025 (2025), Article number 111

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Eigenvalue systems for integer orthogonal bases of multi-matrix invariants at finite $N$


Authors: Adrian Padellaro, Sanjaye Ramgoolam, Ryo Suzuki Projects: C6
Submission Date: 18.10.2024 Submitter: Gernot Akemann
Download: PDF Link: 24060
Published: Journal of High Energy Physics 2025 (2025), Article number 111

24050 Gernot Akemann, Federico Balducci, Aurélia Chenu, Patricia Päßler, Federico Roccati, Ruth Shir PDF

Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking

Project: C6

Published: Phys. Rev. Research 7, no. 1 (2025), 013098

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Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking


Authors: Gernot Akemann, Federico Balducci, Aurélia Chenu, Patricia Päßler, Federico Roccati, Ruth Shir Projects: C6
Submission Date: 23.09.2024 Submitter: Friedrich Götze
Download: PDF Link: 24050
Published: Phys. Rev. Research 7, no. 1 (2025), 013098

24047 Gernot Akemann, Sungsoo Byun, Kohei Noda PDF

Pfaffian structure of the eigenvector overlap for the symplectic Ginibre ensemble

Project: C6

Published: Annales Henri Poincare (2025)

Notes: https://doi.org/10.1007/s00023-025-01575-x

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Pfaffian structure of the eigenvector overlap for the symplectic Ginibre ensemble


Authors: Gernot Akemann, Sungsoo Byun, Kohei Noda Projects: C6
Submission Date: 02.09.2024 Submitter: Friedrich Götze
Download: PDF Link: 24047
Published: Annales Henri Poincare (2025)
Notes: https://doi.org/10.1007/s00023-025-01575-x


All Publications of this Project


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