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Project B5: Universality beyond determinantal point processes


Principal Investigator(s)
Gernot Akemann
Friedrich Götze
Visitor(s)
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Summary:

The project is devoted to a better understanding of generalizations of determinantal point processes, going beyond the classical random matrix ensembles. Prime examples to be studied are so-called beta-ensembles in one and two dimensions, fixed trace ensembles and products of Wigner ensembles. In all settings the key question will be the universality of the logarithmic interaction of eigenvalues, with techniques ranging from concentration of measure and complex analysis to free probability.


Recent Preprints:

20067 Gernot Akemann, Friedrich Götze, Thorsten Neuschel PDF

Characteristic polynomials of products of Wigner matrices: finite-N results and Lyapunov universality

Project: B5

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Characteristic polynomials of products of Wigner matrices: finite-N results and Lyapunov universality


Authors: Gernot Akemann, Friedrich Götze, Thorsten Neuschel Projects: B5
Submission Date: 30.06.2020 Submitter: Michael Baake
Download: PDF Link: 20067

20047 Gernot Akemann, Sungsoo Byun, Nam-Gyu Kang PDF

A non-hermitian generalisation of themarchenko-pastur distribution: from the circular law to multi-criticality

Project: B5

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A non-hermitian generalisation of themarchenko-pastur distribution: from the circular law to multi-criticality


Authors: Gernot Akemann, Sungsoo Byun, Nam-Gyu Kang Projects: B5
Submission Date: 05.05.2020 Submitter: Michael Baake
Download: PDF Link: 20047

20009 Gennadiy P. Chistyakov, Friedrich Götze PDF

Edgeworth-type expansion in the entropic free CLT

Project: B5

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Edgeworth-type expansion in the entropic free CLT


Authors: Gennadiy P. Chistyakov, Friedrich Götze Projects: B5
Submission Date: 31.12.2019 Submitter: Gernot Akemann
Download: PDF Link: 20009

20008 Friedrich Götze, Andrei Zaitsev PDF

Estimates for the closeness of convolutions of probability distributions on convex polyhedra

Project: A4, B5

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Estimates for the closeness of convolutions of probability distributions on convex polyhedra


Authors: Friedrich Götze, Andrei Zaitsev Projects: A4, B5
Submission Date: 31.12.2019 Submitter: Gernot Akemann
Download: PDF Link: 20008

20002 Gernot Akemann, Roger Tribe, Athanasios Tsareas, Oleg Zaboronski PDF

Determinantal structure and bulk universality of conditional overlaps in the complex Ginibre ensemble

Project: B5, C6

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Determinantal structure and bulk universality of conditional overlaps in the complex Ginibre ensemble


Authors: Gernot Akemann, Roger Tribe, Athanasios Tsareas, Oleg Zaboronski Projects: B5, C6
Submission Date: 30.12.2019 Submitter: Friedrich Götze
Download: PDF Link: 20002

20001 Friedrich Götze, Andrei Zaitsev PDF

Rare events and poisson point processes

Project: A4, B5

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Rare events and poisson point processes


Authors: Friedrich Götze, Andrei Zaitsev Projects: A4, B5
Submission Date: 31.12.2019 Submitter: Gernot Akemann
Download: PDF Link: 20001

19105 Gernot Akemann, Yanik-Pascal Förster, Mario Kieburg PDF

Universal eigenvector correlations in quaternionic Ginibre ensembles

Project: B5, C6

Published: Journal of Physics A: Mathematical and Theoretical 53 (2020), 145201: 1–26

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Universal eigenvector correlations in quaternionic Ginibre ensembles


Authors: Gernot Akemann, Yanik-Pascal Förster, Mario Kieburg Projects: B5, C6
Submission Date: 06.12.2019 Submitter: Friedrich Götze
Download: PDF Link: 19105
Published: Journal of Physics A: Mathematical and Theoretical 53 (2020), 145201: 1–26

19104 Tom Claeys, Thorsten Neuschel, Martin Venker PDF

Critical behavior of non-intersecting Brownian motions

Project: B5, C6

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Critical behavior of non-intersecting Brownian motions


Authors: Tom Claeys, Thorsten Neuschel, Martin Venker Projects: B5, C6
Submission Date: 05.12.2019 Submitter: Gernot Akemann
Download: PDF Link: 19104

19026 Taro Nagao, Gernot Akemann, Mario Kieburg, Iván Parra PDF

Families of two-dimensional Coulomb gases on anellipse: correlation functions and universality

Project: B5

Published: Journal of Physics A: Mathematical and Theoretical 53 (2020), 075201: 1–36

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Families of two-dimensional Coulomb gases on anellipse: correlation functions and universality


Authors: Taro Nagao, Gernot Akemann, Mario Kieburg, Iván Parra Projects: B5
Submission Date: 27.05.2019 Submitter: Friedrich Götze
Download: PDF Link: 19026
Published: Journal of Physics A: Mathematical and Theoretical 53 (2020), 075201: 1–36

19025 Gernot Akemann, Taro Nagao, Iván Parra, Graziano Vernizzi PDF

Gegenbauer and other planar orthogonal polynomials on an ellipse in the complex plane

Project: B5

To appear: Constructive Approximation (2020)

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Gegenbauer and other planar orthogonal polynomials on an ellipse in the complex plane


Authors: Gernot Akemann, Taro Nagao, Iván Parra, Graziano Vernizzi Projects: B5
Submission Date: 27.05.2019 Submitter: Friedrich Götze
Download: PDF Link: 19025
To appear: Constructive Approximation (2020)



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