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


Principal Investigator(s)
Gernot Akemann
Visitor(s)
Yan Fyodorov

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:

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 ofcharacter tables

Project: A5, C6

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Row and column detection complexities ofcharacter tables


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

24126 Gernot Akemann, Maurice Duits, Leslie Diëgo Molag PDF

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

Project: C6

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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: 24126

24087 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: 24087
Published: Journal of Physics A: Mathematical and Theoretical 58, no. 12 (2025), 125204

24083 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: 24083
Published: Journal of High Energy Physics 2025 (2025), Article number 111

24068 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: 24068
Published: Phys. Rev. Research 7, no. 1 (2025), 013098

24064 Gernot Akemann, Sungsoo Byun, Kohei Noda PDF

Pfaffian structure of the eigenvector overlap for the symplectic Ginibre ensemble

Project: C6

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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: 24064

24030 Ievgenii Afanasiev, Mariya Shcherbina, Tatyana Shcherbina PDF

Universality of the second correlation function of the deformed Ginibre ensemble

Project: C6

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Universality of the second correlation function of the deformed Ginibre ensemble


Authors: Ievgenii Afanasiev, Mariya Shcherbina, Tatyana Shcherbina Projects: C6
Submission Date: 03.05.2024 Submitter: Gernot Akemann
Download: PDF Link: 24030

23118 Gernot Akemann, Nayden Chakarov, Oliver Krüger, Adam Mielke, Meinolf Ottensmann, Patricia Päßler PDF

Interactions between different birds of prey as a random point process

Project: C6

Published: Journal of Statistical Mechanics 2024 (2024), Article number 053501

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Interactions between different birds of prey as a random point process


Authors: Gernot Akemann, Nayden Chakarov, Oliver Krüger, Adam Mielke, Meinolf Ottensmann, Patricia Päßler Projects: C6
Submission Date: 31.01.2024 Submitter: Michael Baake
Download: PDF Link: 23118
Published: Journal of Statistical Mechanics 2024 (2024), Article number 053501

23096 Sungsoo Byun, Leslie Diëgo Molag, Nick Simm PDF

Large deviations and fluctuations of real eigenvalues of elliptic random matrices

Project: C6

Published: Electronic Journal of Probability 30 (2025), 1–40

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Large deviations and fluctuations of real eigenvalues of elliptic random matrices


Authors: Sungsoo Byun, Leslie Diëgo Molag, Nick Simm Projects: C6
Submission Date: 11.02.2025 Submitter: Gernot Akemann
Download: PDF Link: 23096
Published: Electronic Journal of Probability 30 (2025), 1–40


All Publications of this Project


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