## Zakhar Kabluchko Dissertation

## Prof. Dr. Christoph Thäle

## Research interests

- Stochastic geometry and geometric probability
- Limit theorems for random geometric structures
- Random structures in high dimensions
- Malliavin calculus and Stein's method
- Convex and Integral geometry

## Current teaching

Summer term 2018

**Linear algebra and geometry II**

Tuesday 10-12, HZO 50

Friday 10-12, HZO 50**Random methods in geometry**

Monday 15.00 - 16.30, NA 4/24- Proseminar on
**Planar geometry**

Friday 8-10, NA 2/24

A preliminary discussion of the seminar will take place February 9, 11.30 - 12.00 in room NA 2/99. - Graduate seminar on
**Probability and geometry**

Monday 10-12, NA 1/64 **RTG 2131 seminar**

Monday 17-18, NA 3/99

Winter term 2017/2018

**Vorkurs Mathematik****Linear algebra and geometry I**

Tuesday 10-12, HZO 40

Friday 10-12, HZO 40- Proseminar on
**Symmetries and groups**

Monday 14-16, NA 3/99 - Graduate seminar on
**Probability and geometry**

Monday 10-12, NA 01/99 **RTG 2131 seminar**

Monday 17-18, NA 3/99

## Short CV

I am one of the principal investigators in the Research Training Group (RTG) 2131 High-Dimensional Phenomena in Probability-Fluctuations and Discontinuity.

I am a member of the DFG scientific network Cumulants, concentration and superconcentration

## Editorial activities

I am member of the editorial board of the following journals

## Polyhedron models

I have recently started to build models of polyhedra in 3 and projections of polyhedra in 4 dimensional space. I am still trying to complete this list, but you might check the current status from time to time.

## Publications

**My coauthors:** David Alonso-Gutiérrez, Mareen Beermann, Imre Bárány, Gilles Bonnet, Richard Cowan, Laurent Decreusefond, Christian Deuß, Peter Eichelsbacher, Tobias Fissler, Uta Freiberg, Hans-Otto Georgii (1944-2017), Julian Grote, Jens Grygierek, Julia Hörrmann, Daniel Hug, Zakhar Kabluchko, Kai Krokowski, Günter Last, Christoph Leuenberger, Alexander Marynych, Werner Nagel, Nguyen Ngoc Linh, Giovanni Peccati, Mathew D. Penrose, Bram Petri, Joscha Prochno, Claudia Redenbach, Anselm Reichenbachs, Matthias Reitzner, Tomasz Schreiber (1975-2010), Matthias Schulte, Daniel Temesvari, Nicola Turchi, Viola Weiß, Wolfgang Weil, Elisabeth Werner, Florian Wespi, Marcus Wohler, Joe Yukich

- Cones generated by random points on half-spheres and convex hulls of Poisson point processes (jointly with Zakhar Kabluchko, Alexander Marynych and Daniel Temesvari)

Preprint - Gaussian fluctuations for high-dimensional random projections of ℓ
_{p}^{n}-balls (jointly with David Alonso-Gutiérrez and Joscha Prochno)

Preprint - Limit theorems for random simplices in high dimensions (jointly with Julian Grote and Zakhar Kabluchko)

Preprint - Expected intrinsic volumes and facet numbers of random beta-polytopes (jointly with Zakhar Kabluchko and Daniel Temesvari)

Preprint

Download of the Mathematica notebooks: Random Beta-Polytopes, Random Beta'-Polytopes - Gaussian fluctuations for edge counts in high-dimensional random geometric graphs (jointly with Jens Grygierek)

Preprint - A new quantitative central limit theorem on the Wiener space with applications to Gaussian processes (jointly with Tobias Fissler)

Preprint - Large deviations for high-dimensional random projections of ℓ
_{p}^{n}-balls (jointly with David Alonso-Gutiérrez and Joscha Prochno)

Preprint - Gaussian polytopes: a cumulant-based approach (jointly with Julian Grote)

Preprint - Random polytopes: variances and central limit theorems for intrinsic volumes (jointly with Nicola Turchi and Florian Wespi)

Proceedings of the American Mathematical Society (2017+) - High-dimensional limit theorems for random vectors in ℓ
_{p}^{n}-balls (jointly with Zakhar Kabluchko and Joscha Prochno)

Communications in Contemporary Mathematics (2017+) - Concentration and moderate deviations for Poisson polytopes and polyhedra (jointly with Julian Grote)

Bernoulli (2017+) - Central limit theorem for the volume of random polytopes with vertices on the boundary

Discrete and Computational Geometry (2017+) - Poisson approximation of the length spectrum of random surfaces (jointly with Bram Petri)

Indiana University Mathematics Journal (2016+) - Isotropic constant of random polytopes with vertices on an ℓ
_{p}-sphere (jointly with Julia Hörrmann and Joscha Prochno)

The Journal of Geometric Analysis 28, 405-426 (2018) - Monotonicity of expected f-vectors for projections of regular polytopes (jointly with Zakhar Kabluchko)

Proceedings of the American Mathematical Society 146, 1295-1303 (2018) - Intrinsic volumes and Gaussian polytopes: the missing piece of the jigsaw (jointly with Imre Bárány)

Documenta Mathematica 22, 1323-1335 (2017) - Multivariate central limit theorems for Rademacher functionals with applications (jointly with Kai Krokowski)

Electronic Journal of Probability 22, Article 87 (2017) - A Mecke-type formula and Markov properties for STIT tessellation processes (jointly with Werner Nagel, Linh Ngoc Nguyen and Viola Weiß)

ALEA Latin American Journal of Probability and Mathematical Statistics 14, 691–718 (2017) - Monotonicity of facet numbers of random convex hulls (jointly with Gilles Bonnet, Julian Grote, Daniel Temesvari, Nicola Turchi and Florian Wespi)

Journal of Mathematical Analysis and Applications 455, 1351-1364 (2017) - A random cell splitting scheme on the sphere (jointly with Julia Hörrmann and Christian Deuß)

Stochastic Processes and their Applications 127, 1544–1564 (2017) - Discrete Malliavin-Stein method: Berry-Esseen bounds for random graphs and percolation (jointly with Kai Krokowski and Anselm Reichenbachs)

The Annals of Probability 45, 1071-1109 (2017) - Limit theory for the Gilbert graph (jointly with Matthias Reitzner and Matthias Schulte)

Advances in Applied Mathematics 88, 26–61 (2017) - Central limit theorems for the radial spanning tree (jointly with Matthias Schulte)

Random Structures & Algorithms 50, 262–286 (2017) - Poisson point process convergence and extreme values in stochastic geometry (jointly with Matthias Schulte)

Chapter in the book

Stochastic analysis for Poisson point processes: Malliavin calculus, Wiener-Ito chaos expansions and stochastic geometry

(edited by Giovanni Peccati and Matthias Reitzner)

Springer & Bocconi Series (2016) - Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry (jointly with Laurent Decreusefond and Matthias Schulte)

The Annals of Probability 44, 2147-2197 (2016) - Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences (jointly with Kai Krokowski and Anselm Reichenbachs)

Annales de l’Institut Henri Poincaré, Probabilité et Statistique 52, 763-803 (2016) - Asymptotic theory for statistics of the Poisson-Voronoi approximation (jointly with Joe Yukich)

Bernoulli 22, 2372–2400 (2016) - A four moments theorem for Gamma limits on a Poisson chaos (jointly with Tobias Fissler)

ALEA Latin American Journal of Probability and Mathematical Statistics 13, 163–192 (2016)

Erratum, ALEA Latin American Journal of Probability and Mathematical Statistics 14, 245–247 (2017) - Cumulants on Wiener chaos: moderate deviations and the fourth moment theorem (jointly with Matthias Schulte)

Journal of Functional Analysis 270, 2223–2248 (2016) - The mixing property of STIT tessellations revisited (jointly with Christian Deuß)

North-Western European Journal of Mathematics 2, 1-15 (2016) - Malliavin-Stein method for Variance-Gamma approximation on Wiener space (jointly with Peter Eichelsbacher)

Electronic Journal of Probability 20, Article 123 (2015) - Branching random tessellations with interaction: a thermodynamic view (jointly with Hans-Otto Georgii and Tomasz Schreiber)

The Annals of Probability 43, 1892-1943 (2015) - Poisson polyhedra in high dimensions (jointly with Julia Hörrmann, Daniel Hug and Matthias Reitzner)

Advances in Mathematics 281, 1–39 (2015) - Intersection and proximity for processes of flats (jointly with Daniel Hug and Wolfgang Weil)

Journal of Mathematical Analysis and Applications 426, 1–42 (2015) - New Berry-Esseen bounds for non-linear functionals of Poisson random measures (jointly with Peter Eichelsbacher)

Electronic Journal of Probability 19, Article 102 (2014) - Moments and central limit theorems for some multivariate Poisson functionals (jointly with Günter Last, Mathew D. Penrose and Matthias Schulte)

Advances in Applied Probability 46, 348-364 (2014) - Asymptotic shape of small cells (jointly with Mareen Beermann and Claudia Redenbach)

Mathematische Nachrichten 287, 737-747 (2014) - Distances between Poisson k-flats (jointly with Matthias Schulte)

Methodology and Computing in Applied Probability 16, 311-329 (2014) - The character of planar tessellations which are not side-to-side (jointly with Richard Cowan)

Image Analysis and Stereology 33, 39-54 (2014) - Hausdorff dimension of visibility sets for well-behaved continuum percolation in the hyperbolic plane

Brazilian Journal of Probability and Statistics 28, 73-82 (2014) - Geometry of iteration stable tessellations: Connection with Poisson hyperplanes (jointly with Tomasz Schreiber)

Bernoulli 19, 1637-1654 (2013) - The combinatorial structure of spatial STIT tessellations (jointly with Viola Weiß)

Discrete and Computational Geometry 50, 649-672 (2013) - On the arrangement of cells in planar STIT and Poisson line tessellations (jointly with Claudia Redenbach)

Methodology and Computing in Applied Probability 15, 643-654 (2013) - Exact computation and approximation of stochastic and analytic parameters of generalized Sierpinski gaskets (jointly with Uta Freiberg)

Methodology and Computing in Applied Probability 15, 485-509 (2013) - Gamma limits and U-statistics on the Poisson space (jointly with Giovanni Peccati)

ALEA Latin American Journal of Probability and Mathematical Statistics 10, 525-560 (2013) - Shape-driven nested Markov tessellations (jointly with Tomasz Schreiber)

Stochastics 85, 510-531 (2013) - Limit theorems for iteration stable tessellations (jointly with Tomasz Schreiber)

The Annals of Probability 41, 2261-2278 (2013) - Second-order comparison of three fundamental tessellation models (jointly with Claudia Redenbach)

Statistics 47, 237-257 (2013) - The scaling limit of Poisson-driven order statistics with applications in geometric probability (jointly with Matthias Schulte)

Stochastic Processes and their Applications 122, 4096-4120 (2012) - Second-order theory for iteration stable tessellations (jointly with Tomasz Schreiber)

Probability and Mathematical Statistics 32, 281-300 (2012) - Spatial STIT tessellations: distributional results for I-segments (jointly with Viola Weiss and Werner Nagel)

Advances in Applied Probability 44, 635-654 (2012) - Arak-Clifford-Surgailis tessellations: Basic properties and variance of the total edge length

Journal of Statistical Physics 144, 1329-1339 (2011) - Intrinsic volumes of the maximal polytope process in higher dimensional STIT tessellations (jointly with Tomasz Schreiber)

Stochastic Processes and their Applications 121, 989-1012 (2011) - Supplementary results for length distributions in planar STIT tessellations

Forma 26, 1-6 (2011) - Second-order properties and central limit theory for the vertex process of iteration infinitely divisible and iteration stable random tessellations in the plane (jointly with Tomasz Schreiber)

Advances in Applied Probability 42, 913-935 (2010) - New mean values for homogeneous spatial tessellations that are stable under iteration (jointly with Viola Weiß)

Image Analysis and Stereology 29, 143-157 (2010) - The distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous planar anisotropic STIT tessellations

Commentationes Mathematicae Universitis Carolinae 51, 503-512 (2010) - Moments of the length of line segments in homogeneous planar STIT tessellations

Image Analysis and Stereology 28, 69-76 (2009) - A first attempt to fractal mosaics

Proceedings of the 10th European Conference of ISS.; (V.Capasso et. al. Ed.), The MIRIAM Project Series, Vol. 4, ESCULAPIO Pub. Co., Bologna, Italy (2009) - A Markov chain algorithm for determining crossing times through nested graphs (jointly with Uta Freiberg)

Discrete Mathematics & Theoretical Computer Science, Proc. AI 502-522 (2008) - Birth-time distributions of weighted polytopes in STIT tessellations (jointly with Nguyen Ngoc Linh)

unpublished manuscript - Exact and asymptotic results for intrinsic volumes of Poisson k-flat processes (jointly with Matthias Schulte)

unpublished manuscript

**Other texts**

## Completed theses

Here is a list of completed bachelor, master/diploma and PhD theses

## Address

Prof. Dr. Christoph Thäle

Faculty of Mathematics

Ruhr University Bochum

Room N-SÜD 1/51

44780 Bochum

Germany

Phone: 0234 - 32 - 28988

Consultation-hour: Monday 9-10 (during the semester) and by appointment (during the semester breaks)

Monotonicity of expected -vectors for projections of regular polytopes

Authors:Zakhar Kabluchko and Christoph Thäle

Journal: Proc. Amer. Math. Soc. **146** (2018), 1295-1303

MSC (2010): Primary 52A22, 60D05; Secondary 52B11, 52A20, 51M20

DOI: https://doi.org/10.1090/proc/13827

Published electronically: October 6, 2017

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be an -dimensional regular polytope from one of the three infinite series (regular simplices, regular crosspolytopes, and cubes). Project onto a random, uniformly distributed linear subspace of dimension . We prove that the expected number of -dimensional faces of the resulting random polytope is an increasing function of . As a corollary, we show that the expected number of -faces of the Gaussian polytope is an increasing function of the number of points used to generate the polytope. Similar results are obtained for the symmetric Gaussian polytope and the Gaussian zonotope.

**[1]**Fernando Affentranger and Rolf Schneider,*Random projections of regular simplices*, Discrete Comput. Geom.**7**(1992), no. 3, 219-226. MR**1149653**, https://doi.org/10.1007/BF02187839**[2]**Yuliy M. Baryshnikov and Richard A. Vitale,*Regular simplices and Gaussian samples*, Discrete Comput. Geom.**11**(1994), no. 2, 141-147. MR**1254086**, https://doi.org/10.1007/BF02574000- [3] Mareen Beermann,
*Random Polytopes*, Ph.D. thesis, University of Osnabrück, 2015, Available at: . - [4] Mareen Beermann and Matthias Reitzner,
*Monotonicity of functionals of random polytopes*, In: G. Ambrus, K. Böröczky, and Z. Füredi, (eds.): Discrete Geometry and Convexity, pp. 23-28, A. Rényi Institute of Mathematics, Hungarian Academy of Sciences, 2017, preprint available at http://arxiv.org/abs/1706.08342. **[5]**Marcel Berger,*Geometry. II*, Universitext, Springer-Verlag, Berlin, 1987. Translated from the French by M. Cole and S. Levy. MR**882916****[6]**Ulrich Betke and Martin Henk,*Intrinsic volumes and lattice points of crosspolytopes*, Monatsh. Math.**115**(1993), no. 1-2, 27-33. MR**1223242**, https://doi.org/10.1007/BF01311208**[7]**Johannes Böhm and Eike Hertel,*Polyedergeometrie in -dimensionalen Räumen konstanter Krümmung*, Lehrbücher und Monographien aus dem Gebiete der Exakten Wissenschaften (LMW). Mathematische Reihe [Textbooks and Monographs in the Exact Sciences. Mathematical Series], vol. 70, Birkhäuser Verlag, Basel-Boston, Mass., 1981 (German). MR**626823****[8]**Gilles Bonnet, Julian Grote, Daniel Temesvari, Christoph Thäle, Nicola Turchi, and Florian Wespi,*Monotonicity of facet numbers of random convex hulls*, J. Math. Anal. Appl.**455**(2017), no. 2, 1351-1364. MR**3671230**, https://doi.org/10.1016/j.jmaa.2017.06.054**[9]**Károly Böröczky Jr. and Martin Henk,*Random projections of regular polytopes*, Arch. Math. (Basel)**73**(1999), no. 6, 465-473. MR**1725183**, https://doi.org/10.1007/s000130050424**[10]**Olivier Devillers, Marc Glisse, Xavier Goaoc, Guillaume Moroz, and Matthias Reitzner,*The monotonicity of -vectors of random polytopes*, Electron. Commun. Probab.**18**(2013), no. 23, 8. MR**3044471**, https://doi.org/10.1214/ECP.v18-2469**[11]**David L. Donoho and Jared Tanner,*Counting faces of randomly projected polytopes when the projection radically lowers dimension*, J. Amer. Math. Soc.**22**(2009), no. 1, 1-53. MR**2449053**, https://doi.org/10.1090/S0894-0347-08-00600-0**[12]**David L. Donoho and Jared Tanner,*Counting the faces of randomly-projected hypercubes and orthants, with applications*, Discrete Comput. Geom.**43**(2010), no. 3, 522-541. MR**2587835**, https://doi.org/10.1007/s00454-009-9221-z**[13]**Branko Grünbaum,*Convex polytopes*, 2nd ed., Graduate Texts in Mathematics, vol. 221, Springer-Verlag, New York, 2003. Prepared and with a preface by Volker Kaibel, Victor Klee and Günter M. Ziegler. MR**1976856****[14]**Daniel Hug, Götz Olaf Munsonius, and Matthias Reitzner,*Asymptotic mean values of Gaussian polytopes*, Beiträge Algebra Geom.**45**(2004), no. 2, 531-548. MR**2093024****[15]**K. Leichtweiss,*Konvexe Mengen*, Hochschulbücher für Mathematik [University Books for Mathematics], 81, VEB Deutscher Verlag der Wissenschaften, Berlin, 1980 (German). MR**559138****[16]**Harold Ruben,*On the geometrical moments of skew-regular simplices in hyperspherical space, with some applications in geometry and mathematical statistics*, Acta Math.**103**(1960), 1-23. MR**0121713**, https://doi.org/10.1007/BF02546523**[17]**Rolf Schneider,*Convex bodies: the Brunn-Minkowski theory*, Second expanded edition, Encyclopedia of Mathematics and its Applications, vol. 151, Cambridge University Press, Cambridge, 2014. MR**3155183****[18]**Rolf Schneider and Wolfgang Weil,*Stochastic and integral geometry*, Probability and its Applications (New York), Springer-Verlag, Berlin, 2008. MR**2455326****[19]**A. M. Vershik and P. V. Sporyshev,*Asymptotic behavior of the number of faces of random polyhedra and the neighborliness problem*, Selecta Math. Soviet.**11**(1992), no. 2, 181-201. Selected translations. MR**1166627****[20]**V. H. Vu,*Sharp concentration of random polytopes*, Geom. Funct. Anal.**15**(2005), no. 6, 1284-1318. MR**2221249**, https://doi.org/10.1007/s00039-005-0541-8

## References

**[1]**- Fernando Affentranger and Rolf Schneider,
*Random projections of regular simplices*, Discrete Comput. Geom.**7**(1992), no. 3, 219-226. MR**1149653**, https://doi.org/10.1007/BF02187839 **[2]**- Yuliy M. Baryshnikov and Richard A. Vitale,
*Regular simplices and Gaussian samples*, Discrete Comput. Geom.**11**(1994), no. 2, 141-147. MR**1254086**, https://doi.org/10.1007/BF02574000 - [3]
- Mareen Beermann,
*Random Polytopes*, Ph.D. thesis, University of Osnabrück, 2015, Available at: . - [4]
- Mareen Beermann and Matthias Reitzner,
*Monotonicity of functionals of random polytopes*, In: G. Ambrus, K. Böröczky, and Z. Füredi, (eds.): Discrete Geometry and Convexity, pp. 23-28, A. Rényi Institute of Mathematics, Hungarian Academy of Sciences, 2017, preprint available at http://arxiv.org/abs/1706.08342. **[5]**- Marcel Berger,
*Geometry. II*, Universitext, Springer-Verlag, Berlin, 1987. Translated from the French by M. Cole and S. Levy. MR**882916** **[6]**- Ulrich Betke and Martin Henk,
*Intrinsic volumes and lattice points of crosspolytopes*, Monatsh. Math.**115**(1993), no. 1-2, 27-33. MR**1223242**, https://doi.org/10.1007/BF01311208 **[7]**- Johannes Böhm and Eike Hertel,
*Polyedergeometrie in -dimensionalen Räumen konstanter Krümmung*, Lehrbücher und Monographien aus dem Gebiete der Exakten Wissenschaften (LMW). Mathematische Reihe [Textbooks and Monographs in the Exact Sciences. Mathematical Series], vol. 70, Birkhäuser Verlag, Basel-Boston, Mass., 1981 (German). MR**626823** **[8]**- Gilles Bonnet, Julian Grote, Daniel Temesvari, Christoph Thäle, Nicola Turchi, and Florian Wespi,
*Monotonicity of facet numbers of random convex hulls*, J. Math. Anal. Appl.**455**(2017), no. 2, 1351-1364. MR**3671230**, https://doi.org/10.1016/j.jmaa.2017.06.054 **[9]**- Károly Böröczky Jr. and Martin Henk,
*Random projections of regular polytopes*, Arch. Math. (Basel)**73**(1999), no. 6, 465-473. MR**1725183**, https://doi.org/10.1007/s000130050424 **[10]**- Olivier Devillers, Marc Glisse, Xavier Goaoc, Guillaume Moroz, and Matthias Reitzner,
*The monotonicity of -vectors of random polytopes*, Electron. Commun. Probab.**18**(2013), no. 23, 8. MR**3044471**, https://doi.org/10.1214/ECP.v18-2469 **[11]**- David L. Donoho and Jared Tanner,
*Counting faces of randomly projected polytopes when the projection radically lowers dimension*, J. Amer. Math. Soc.**22**(2009), no. 1, 1-53. MR**2449053**, https://doi.org/10.1090/S0894-0347-08-00600-0 **[12]**- David L. Donoho and Jared Tanner,
*Counting the faces of randomly-projected hypercubes and orthants, with applications*, Discrete Comput. Geom.**43**(2010), no. 3, 522-541. MR**2587835**, https://doi.org/10.1007/s00454-009-9221-z **[13]**- Branko Grünbaum,
*Convex polytopes*, 2nd ed., Graduate Texts in Mathematics, vol. 221, Springer-Verlag, New York, 2003. Prepared and with a preface by Volker Kaibel, Victor Klee and Günter M. Ziegler. MR**1976856** **[14]**- Daniel Hug, Götz Olaf Munsonius, and Matthias Reitzner,
*Asymptotic mean values of Gaussian polytopes*, Beiträge Algebra Geom.**45**(2004), no. 2, 531-548. MR**2093024** **[15]**- K. Leichtweiss,
*Konvexe Mengen*, Hochschulbücher für Mathematik [University Books for Mathematics], 81, VEB Deutscher Verlag der Wissenschaften, Berlin, 1980 (German). MR**559138** **[16]**- Harold Ruben,
*On the geometrical moments of skew-regular simplices in hyperspherical space, with some applications in geometry and mathematical statistics*, Acta Math.**103**(1960), 1-23. MR**0121713**, https://doi.org/10.1007/BF02546523 **[17]**- Rolf Schneider,
*Convex bodies: the Brunn-Minkowski theory*, Second expanded edition, Encyclopedia of Mathematics and its Applications, vol. 151, Cambridge University Press, Cambridge, 2014. MR**3155183** **[18]**- Rolf Schneider and Wolfgang Weil,
*Stochastic and integral geometry*, Probability and its Applications (New York), Springer-Verlag, Berlin, 2008. MR**2455326** **[19]**- A. M. Vershik and P. V. Sporyshev,
*Asymptotic behavior of the number of faces of random polyhedra and the neighborliness problem*, Selecta Math. Soviet.**11**(1992), no. 2, 181-201. Selected translations. MR**1166627** **[20]**- V. H. Vu,
*Sharp concentration of random polytopes*, Geom. Funct. Anal.**15**(2005), no. 6, 1284-1318. MR**2221249**, https://doi.org/10.1007/s00039-005-0541-8

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Additional Information **Zakhar Kabluchko**

Affiliation: Institut für Mathematische Stochastik, Westfälische Wilhelms-Universität Münster, Orléans-Ring 10, 48149 Münster, Germany

Email: zakhar.kabluchko@uni-muenster.de **Christoph Thäle**

Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany

Email: christoph.thaele@rub.de

DOI: https://doi.org/10.1090/proc/13827

Keywords: Convex hull, Gaussian polytope, Gaussian zonotope, Goodman--Pollack model, $f$-vector, random polytope, regular polytope

Received by editor(s): April 26, 2017

Published electronically: October 6, 2017

Communicated by: David Levin

Article copyright: © Copyright 2017 American Mathematical Society

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