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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.
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21065
Friedrich Götze, Mindaugas Bloznelis PDF
Edgeworth approximations for distributions of symmetric statistics Project: B5 Published: Probab. Theory Relat. Fields 183 (2022), 1153–1235 |
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21027
Sergey Bobkov, Maria Danshina, Vladimir Ulyanov PDF
On rate of convergence to the Poisson law of the number of cycles in the generalized random graphs Project: B5 Published: Operator theory and harmonic analysis—OTHA 2020. Part II. Probability-analytical models, methods and applications (2021), 109–133
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On rate of convergence to the Poisson law of the number of cycles in the generalized random graphs |
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20122
Friedrich Götze, Alexey Naumov, Alexander Tikhomirov PDF
Local semicircle law under fourth moment condition Project: B5 Published: Journal of Theoretical Probability 33 (2020), 1327–1362 Notes: DOI: 10.1007/s10959-019-00907-y |
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20118
Friedrich Götze, Zakhar Kabluchko, Dmitry Zaporozhets PDF
Grassmann angles and absorption probabilities of Gaussian convex hulls Project: B5 |
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20117
Friedrich Götze, Andrei Zaitsev PDF
Project: B5
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On alternative approximating distributions in the multivariate version of Kolmogorov's second uniform limit theorem |
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20116
Gennadiy P. Chistyakov, Friedrich Götze PDF
Approximation of free convolutions by free infinitely divisible laws Project: B5 |
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20067
Gernot Akemann, Friedrich Götze, Thorsten Neuschel PDF
Project: B5 Published: Electronic Communications in Probability 26 (2021), Article No. 30: 13 pp.
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Characteristic polynomials of products of Wigner matrices: finite-N results and Lyapunov universality |
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20047
Gernot Akemann, Sungsoo Byun, Nam-Gyu Kang PDF
Project: B5 Published: Annales Henri Poincaré, Integrable Probability and Random Matrices (2020), 34 pages
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A non-hermitian generalisation of themarchenko-pastur distribution: from the circular law to multi-criticality |
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20009
Gennadiy P. Chistyakov, Friedrich Götze PDF
Edgeworth-type expansion in the entropic free CLT Project: B5 |
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20008
Friedrich Götze, Andrei Zaitsev PDF
Estimates for the closeness of convolutions of probability distributions on convex polyhedra Published: Journal of Mathematical Sciences 251 (2020), 67–73 |
