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Project A4.1: Measure concentration and information distances


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Summary:

In this project we shall investigate concentration of measure and large deviation tail bounds for Lipschitz type functions of high dimensional vectors of observations for various distribution classes. The large deviation behavior of functions on Euclidean spaces and on metric spaces and graphs is studied by means of gradients respectively finite differences. Furthermore, we shall investigate the convergence in the central limit theorem for sums of independent random elements in classical, non commutative and related probability theories in terms of appropriate information distances.


Recent Preprints:

20133 Holger Sambale, Arthur Sinulis PDF

Concentration inequalities on the multislice and for sampling without replacement

Project: A4

Published: Journal of Theoretical Probability 35 (2022), 2712–2737

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Concentration inequalities on the multislice and for sampling without replacement


Authors: Holger Sambale, Arthur Sinulis Projects: A4
Submission Date: 05.01.2021 Submitter: Gernot Akemann
Download: PDF Link: 20133
Published: Journal of Theoretical Probability 35 (2022), 2712–2737

20132 Matthias Löwe, Holger Sambale, Holger Knöpfel PDF

Large deviations and a phase transition in the Block Spin Potts models

Project: A4

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Large deviations and a phase transition in the Block Spin Potts models


Authors: Matthias Löwe, Holger Sambale, Holger Knöpfel Projects: A4
Submission Date: 05.01.2021 Submitter: Gernot Akemann
Download: PDF Link: 20132

20121 Sergey Bobkov, Gennadiy P. Chistyakov, Friedrich Götze PDF

Normal Approximation for Weighted Sums under a Second-Order Correlation Condition

Project: A4

Published: Ann. Probab. 48, no. 3 (2020), 1202–1219

Notes: DOI: 10.1214/19-AOP1388

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Normal Approximation for Weighted Sums under a Second-Order Correlation Condition


Authors: Sergey Bobkov, Gennadiy P. Chistyakov, Friedrich Götze Projects: A4
Submission Date: 30.12.2020 Submitter: Gernot Akemann
Download: PDF Link: 20121
Published: Ann. Probab. 48, no. 3 (2020), 1202–1219
Notes: DOI: 10.1214/19-AOP1388

20120 Sergey Bobkov, Gennadiy P. Chistyakov, Friedrich Götze PDF

Non-Uniform Bounds in the Poisson Approximation with Applications to Informational Distances. II

Project: A4

Published: Lithuanian Mathematical Journal 59, no. 4 (2019), 469–497

Notes: DOI: 10.1007/s10986-019-09468-3

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Non-Uniform Bounds in the Poisson Approximation with Applications to Informational Distances. II


Authors: Sergey Bobkov, Gennadiy P. Chistyakov, Friedrich Götze Projects: A4
Submission Date: 30.12.2020 Submitter: Gernot Akemann
Download: PDF Link: 20120
Published: Lithuanian Mathematical Journal 59, no. 4 (2019), 469–497
Notes: DOI: 10.1007/s10986-019-09468-3

20119 Friedrich Götze, Sergey Bobkov, Gennadiy P. Chistyakov PDF

Non-uniform Bounds in the Poisson Approximation with Applications to Informational Distances. I

Project: A4

Published: IEEE Transactions on Information Theory 65, no. 9 (2019), 5283–5293

Notes: DOI: 10.1109/TIT.2019.2913313

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Non-uniform Bounds in the Poisson Approximation with Applications to Informational Distances. I


Authors: Friedrich Götze, Sergey Bobkov, Gennadiy P. Chistyakov Projects: A4
Submission Date: 30.12.2020 Submitter: Gernot Akemann
Download: PDF Link: 20119
Published: IEEE Transactions on Information Theory 65, no. 9 (2019), 5283–5293
Notes: DOI: 10.1109/TIT.2019.2913313

20115 Sergey Bobkov, Gennadiy P. Chistyakov, Friedrich Götze PDF

Poincaré Inequalities and Normal Approximation for Weighted Sums

Project: A4

Published: Electronic Journal of Probability 25, no. 155 (2020), 31 pp

Notes: DOI: 10.1214/20-EJP549

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Poincaré Inequalities and Normal Approximation for Weighted Sums


Authors: Sergey Bobkov, Gennadiy P. Chistyakov, Friedrich Götze Projects: A4
Submission Date: 30.12.2020 Submitter: Gernot Akemann
Download: PDF Link: 20115
Published: Electronic Journal of Probability 25, no. 155 (2020), 31 pp
Notes: DOI: 10.1214/20-EJP549

20098 Anna Gusakova, Holger Sambale, Christoph Thäle PDF

Concentration on Poisson spaces via modified $\Phi$-Sobolev inequalities

Project: A4

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Concentration on Poisson spaces via modified $\Phi$-Sobolev inequalities


Authors: Anna Gusakova, Holger Sambale, Christoph Thäle Projects: A4
Submission Date: 03.09.2020 Submitter: Gernot Akemann
Download: PDF Link: 20098

20053 Holger Sambale PDF

Some notes on concentration for $\alpha$-subexponential random variables

Project: A4

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Some notes on concentration for $\alpha$-subexponential random variables


Authors: Holger Sambale Projects: A4
Submission Date: 19.05.2020 Submitter: Gernot Akemann
Download: PDF Link: 20053

20010 Friedrich Götze, Andrei Zaitsev, Dmitry Zaporozhets PDF

A multivariate version of Kolmogorov's second uniform limit theorem

Project: A4

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A multivariate version of Kolmogorov's second uniform limit theorem


Authors: Friedrich Götze, Andrei Zaitsev, Dmitry Zaporozhets Projects: A4
Submission Date: 31.12.2019 Submitter: Gernot Akemann
Download: PDF Link: 20010

20008 Friedrich Götze, Andrei Zaitsev PDF

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

Project: A4, B5

Published: Journal of Mathematical Sciences 251 (2020), 67–73

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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
Published: Journal of Mathematical Sciences 251 (2020), 67–73


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