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Project B1: Asymptotic distributions, lattices and groups



Summary:

In this project F. Götze will study the distribution of definite as well as indefinite forms of second and higher order on lattices in connection with lattice point problems, diophantine inequalities and the so-called quantum chaos problem. The methods developed here apply as well to approximation results for nonlinear statistics of random variables in probability theory. The investigation of indefinite forms leads to dynamical and geometric problems for linear algebraic groups as well as for their arithmetic and geometrically relevant discrete subgroups and the corresponding homogeneous spaces which will be studied by H. Abels. Here the focus is on problems by Auslander, Milnor and Siegel and the geometry of reductive groups. Joint research efforts will be devoted to the study of generic and stochastic distribution properties of eigenvectors as well as to open problems related to effective bounds for the quantitative Oppenheim-conjecture. Several of the research topics mentioned will be studied in collaboration with G.A. Margulis.



Recent Preprints:

17005 Marek Bozejko, Światosław R. Gal, Wojciech Młotkowski PDF

Positive definite functions on Coxeter groups with applications to operator spaces and noncommutative probability

Project: B1

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Positive definite functions on Coxeter groups with applications to operator spaces and noncommutative probability


Authors: Marek Bozejko, Światosław R. Gal, Wojciech Młotkowski Projects: B1
Submission Date: 2017-03-07 Submitter: Friedrich Götze
Download: PDF Link: 17005

16054 Friedrich Götze, Anna Gusakova PDF

On algebraic integers in short intervals and near smooth curves

Project: B1

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On algebraic integers in short intervals and near smooth curves


Authors: Friedrich Götze, Anna Gusakova Projects: B1
Submission Date: 2016-12-23 Submitter: Kai-Uwe Bux
Download: PDF Link: 16054

16053 Vasili Bernik, Friedrich Götze, Anna Gusakova PDF

On points with algebraically conjugate coordinates close to smooth curves

Project: B1

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On points with algebraically conjugate coordinates close to smooth curves


Authors: Vasili Bernik, Friedrich Götze, Anna Gusakova Projects: B1
Submission Date: 2016-12-23 Submitter: Kai-Uwe Bux
Download: PDF Link: 16053

16052 Vasili Bernik, Friedrich Götze, Anna Gusakova PDF

On distribution of points with algebraically conjugate coordinates in neighborhood of smooth curves

Project: B1

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On distribution of points with algebraically conjugate coordinates in neighborhood of smooth curves


Authors: Vasili Bernik, Friedrich Götze, Anna Gusakova Projects: B1
Submission Date: 2016-12-23 Submitter: Kai-Uwe Bux
Download: PDF Link: 16052

16051 Sergey Bobkov, Gennadiy P. Chistyakov, Friedrich Götze PDF

Stability of Cramer’s characterization of normal laws in information distances

Project: B1

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Stability of Cramer’s characterization of normal laws in information distances


Authors: Sergey Bobkov, Gennadiy P. Chistyakov, Friedrich Götze Projects: B1
Submission Date: 2016-12-23 Submitter: Holger Kösters
Download: PDF Link: 16051

16050 Friedrich Götze, Denis Koleda, Dmitry Zaporozhets PDF

Correlations between real and complex zeros of a random polynomial

Project: B1

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Correlations between real and complex zeros of a random polynomial


Authors: Friedrich Götze, Denis Koleda, Dmitry Zaporozhets Projects: B1
Submission Date: 2016-12-23 Submitter: Holger Kösters
Download: PDF Link: 16050

16046 Friedrich Götze, Andrei Zaitsev PDF

New applications of Arak’s inequalities to the Littlewood–Offord problem

Project: B1

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New applications of Arak’s inequalities to the Littlewood–Offord problem


Authors: Friedrich Götze, Andrei Zaitsev Projects: B1
Submission Date: 2016-12-23 Submitter: Holger Kösters
Download: PDF Link: 16046

16035 Ulf Rehmann, Ernest Vinberg PDF

On a phenomenon discovered by Heinz Helling

Project: B1

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On a phenomenon discovered by Heinz Helling


Authors: Ulf Rehmann, Ernest Vinberg Projects: B1
Submission Date: 2016-09-13 Submitter: Herbert Abels
Download: PDF Link: 16035

15081 Sergey Bobkov, Gennadiy P. Chistyakov, Friedrich Götze PDF

Second order concentration on the sphere

Project: B1

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Second order concentration on the sphere


Authors: Sergey Bobkov, Gennadiy P. Chistyakov, Friedrich Götze Projects: B1
Submission Date: 2015-12-16 Submitter: Michael Röckner
Download: PDF Link: 15081

15080 Sergey Bobkov, Gennadiy P. Chistyakov, Friedrich Götze PDF

Regularized Distributions and Entropic Stability of Cramer's Characterization of the Normal Law

Project: B1

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Regularized Distributions and Entropic Stability of Cramer's Characterization of the Normal Law


Authors: Sergey Bobkov, Gennadiy P. Chistyakov, Friedrich Götze Projects: B1
Submission Date: 2015-12-16 Submitter: Michael Röckner
Download: PDF Link: 15080



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