Publications
Preprints
A Blaschke-Petkantschin formula for linear and affine subspaces with application to intersection probabilities
jointly with Emil Dare and Markus KiderlenWeighted floating functions and weighted functional affine surface areas
jointly with Carsten Schütt, Nicola Turchi and Elisabeth WernerQuantification of the fourth moment theorem for cyclotomic generating functions
jointly with Benedikt RednoßVertex number of the typical cell in a tri-directional Poisson line tessellation
jointly with Nils Heerten and Janina HübnerA note on critical intersections of classical and Schatten p-balls
jointly with Mathias SonnleitnerModerate deviations on Poisson chaos
jointly with Matthias SchulteA quantitative central limit theorem for Poisson horospheres in high dimensions
jointly with Zakhar Kabluchko and Daniel Rosen
Publications since 2020
Large deviations for hyperbolic k-nearest neighbor balls
jointly with Christian Hirsch, Moritz Otto and Takashi Owada
Annales de l’Institut Henri Poincaré, Probabilité et Statistique (2023+)Sharpening the probabilistic arithmetic-geometric mean Inequality
jointly with Tom Kaufmann
Proceedings of the American Mathematical Society (2023+)Fluctuations of λ-geodesic Poisson hyperplanes in hyperbolic space
jointly with Zakhar Kabluchko and Daniel Rosen
Israel Journal of Mathematics (2023+)Spherical convex hull of random points on a wedge
jointly with Florian Besau, Anna Gusakova, Matthias Reitzner, Carsten Schütt and Elisabeth Werner
Mathematische Annalen (2023+)Probabilistic limit theorems induced by the zeros of polynomials
jointly with Nils Heerten and Holger Sambale
Mathematische Nachrichten 297, 1772-1792 (2024)Asymptotic expected T-functionals of random polytopes with applications to Lp surface areas
jointly with Steven Hoehner, Ben Li and Michael Roysdon
Mathematische Nachrichten 297, 914-931 (2024)The proportion of triangles in a class of anisotropic Poisson line tessellations
jointly with Nils Heerten and Julia Krecklenberg
Journal of Applied Probability 61, 214-229 (2024)Sectional Voronoi tessellations: Characterization and high-dimensional limits
jointly with Anna Gusakova and Zakhar Kabluchko
Bernoulli 30, 1482-1501 (2024)Approaching the coupon collector's problem with group drawings via Stein's method
jointly with Carina Betken
Journal of Applied Probability 60, 1352-1366 (2023)Intersections of Poisson k-flats in constant curvature spaces
jointly with Carina Betken and Daniel Hug
Stochastic Processes and their Applications 165, 96-129 (2023)Large nearest neighbour balls in hyperbolic stochastic geometry
jointly with Moritz Otto
Extremes 26, 413-431 (2023)Variance expansion and Berry-Esseen bound for the number of vertices of a random polygon in a polygon
jointly with Anna Gusakova and Matthias Reitzner
Annales Henri Lebesgue 6, 875-906 (2023)The volume of random simplices from elliptical distributions in high dimension
jointly with Anna Gusakova and Johannes Heiny
Stochastic Processes and their Applications 164, 357-382 (2023)The β-Delaunay tessellation IV: Mixing properties and central limit theorems
jointly with Anna Gusakova and Zakhar Kabluchko
Stochastics and Dynamics 23 (2023), article 2350021, 38 pagesSecond-order properties for planar Mondrian tessellations
jointly with Carina Betken, Tom Kaufmann and Kathrin Meier
Methodology and Computing in Applied Probability 25 (2023), article 47, 28 pagesA simplified second-order Gaussian Poincaré inequality in discrete setting with applications
jointly with Peter Eichelsbacher, Benedikt Rednoß and Guangqu Zheng
Annales de l’Institut Henri Poincaré, Probabilité et Statistique 59, 271-302 (2023)Large deviations for uniform projections of p-radial distributions on ℓpn-balls
jointly with Tom Kaufmann and Holger Sambale
Probability and Mathematical Statistics 42, 303-317 (2022)The β-Delaunay tessellation I: Description of the model and geometry of typical cells
jointly with Anna Gusakova and Zakhar Kabluchko
Advances in Applied Probability 54, 1252-1290 (2022)Limit theorems for random points in a simplex
jointly with Anastas Baci, Zakhar Kabluchko, Joscha Prochno and Mathias Sonnleitner
Journal of Applied Probability 59, 685-701 (2022)Random cones in high dimensions I: Donoho-Tanner and Cover-Efron cones
jointly with Thomas Godland and Zakhar Kabluchko
Discrete Analysis (2022), article 5, 44 pagesVariance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes
jointly with Carina Betken and Matthias Schulte
Electronic Journal of Probability 27 (2022), 47 pagesWeighted p-radial distributions on Euclidean and matrix p-balls with applications to large deviations
jointly with Tom Kaufmann
Journal of Mathematical Analysis and Applications 515 (2022), article 126377, 41 pagesWeak convergence of the intersection point process of Poisson hyperplanes
jointly with Anastas Baci and Gilles Bonnet
Annales de l’Institut Henri Poincaré, Probabilité et Statistique 58, 1208-1227 (2022)Random cones in high dimensions II: Weyl cones
jointly with Thomas Godland and Zakhar Kabluchko
Mathematika 68, 710-737 (2022)The β-Delaunay tessellation II: The Gaussian limit tessellation
jointly with Anna Gusakova and Zakhar Kabluchko
Electronic Journal of Probability 27, article 62 (2022), 33 pagesBeta-star polytopes and hyperbolic stochastic geometry
jointly with Thomas Godland and Zakhar Kabluchko
Advances in Mathematics 404, article 108382 (2022), 69 pagesOptimal Variance-Gamma approximation on the second Wiener chaos
jointly with Ehsan Azmoodehsan and Peter Eichelsbacher
Journal of Functional Analysis 282, article 109450 (2022)Multi-dimensional normal approximation of heavy-tailed moving averages
jointly with Ehsan Azmoodeh and Mathias Mørck Ljungdahl
Stochastic Processes and their Applications 145, 308-334 (2022)The β-Delaunay tessellation III: Kendall's problem and limit theorems in high dimensions
jointly with Anna Gusakova and Zakhar Kabluchko
ALEA Latin American Journal of Probability and Mathematical Statistics 19, 23-50 (2022)A new approach to weak convergence of random cones and polytopes
jointly with Zakhar Kabluchko and Daniel Temesvari
Canadian Journal of Mathematics 73, 1627-1647 (2021)Random inscribed polytopes in projective geometries
jointly with Florian Besau and Daniel Rosen
Mathematische Annalen 381, 1345-1372 (2021)Another note on the inequality between geometric and p-generalized arithmetic mean
Mathematische Nachrichten 294, 1977-1986 (2021)The typical cell of a Voronoi tessellation on the sphere
jointly with Zakhar Kabluchko
Discrete and Computational Geometry 66, pages 1330-1350 (2021)Concentration on Poisson spaces via modified Φ-Sobolev inequalities
jointly with Anna Gusakova and Holger Sambale
Stochastic Processes and their Applications 140, 216-235 (2021)Sharp inequalities for the mean distance of random points in convex bodies
jointly with Gilles Bonnet, Anna Gusakova and Dmitry Zaporozhets
Advances in Mathematics 386, article 107813 (2021), 27 pagesA new look at random projections of the cube and general product measures
jointly with Zakhar Kabluchko and Joscha Prochno
Bernoulli 27, 2117-2138 (2021)Surface area deviation between smooth convex bodies and polytopes
jointly with Julian Grote and Elisabeth Werner
Advances in Applied Mathematics 129, article 102218 (2021), 25 pagesDoes a central limit theorem hold for the k-skeleton of Poisson hyperplanes in hyperbolic space?
jointly with Felix Herold and Daniel Hug
Probability Theory and Related Fields 179, 889–968 (2021)On random convex chains, orthogonal polynomials, PF sequences and probabilistic limit theorems
jointly with Anna Gusakova
Mathematika 67, 434-446 (2021)High-dimensional limit theorems for random vectors in ℓpn-balls. II
jointly with Zakhar Kabluchko and Joscha Prochno
Communications in Contemporary Mathematics 23, article 1950073 (2021), 35 pagesThe volume of simplices in high-dimensional Poisson-Delaunay tessellations
jointly with Anna Gusakova
Annales Henri Lebesgue 4, 121-153 (2021)Faces in random great hypersphere tessellations
jointly with Zakhar Kabluchko
Electronic Journal of Probability, article 3 (2021), 35 pagesAsymptotic normality for random simplices and convex bodies in high dimensions
jointly with David Alonso-Gutiérrez, Florian Besau, Julian Grote, Zakhar Kabluchko, Matthias Reitzner, Beatrice-Helen Vritsiou and Elisabeth Werner
Proceedings of the American Mathematical Society 149, 355–367 (2021)Large deviations, moderate deviations, and the KLS conjecture
jointly with David Alonso-Gutiérrez and Joscha Prochno
Journal of Functional Analysis 280, article 108779 (2021), 33 pagesIntersection of unit balls in classical matrix ensembles
jointly with Zakhar Kabluchko and Joscha Prochno
Israel Journal of Mathematics 239, 129–172 (2020)Concentration inequalities for functionals of Poisson cylinder processes
jointly with Anastas Baci, Carina Betken and Anna Gusakova
Electronic Journal of Probability, article 128 (2020), 27 pagesAsymptotic normality for random polytopes in non-Euclidean geometries
jointly with Florian Besau
Transactions of the American Mathematical Society 373, 8911-8941 (2020)Beta polytopes and Poisson polyhedra: f-vectors and angles
jointly with Zakhar Kabluchko and Dmitry Zaporozhets
Advances in Mathematics 374, article 107333 (2020), 63 pagesExact asymptotic volume and volume ratio of Schatten unit balls
jointly with Zakhar Kabluchko and Joscha Prochno
Journal of Approximation Theory 257, article 105457 (2020), 13 pagesSanov-type large deviations in Schatten classes
jointly with Zakhar Kabluchko and Joscha Prochno
Annales de l’Institut Henri Poincaré, Probabilité et Statistique 56, 928–953 (2020)A Berry-Esseén theorem for partial sums of functionals of heavy-tailed moving averages
jointly with Andreas Basse-O'Connor and Mark Podolskij
Electronic Journal of Probability 25, article 31 (2020), 31 pagesGaussian fluctuations for edge counts in high-dimensional random geometric graphs
jointly with Jens Grygierek
Statistics and Probability Letters 158, 108674 (2020)
Publications 2015-2020
Geometry of ℓpn-balls: Classical results and recent developments
jointly with Joscha Prochno and Nicola Turchi
Chapter in the book High Dimensional Probability VIII. The Oaxaca Volume (edited by N. Gozlan, R. Latala, K. Lounici and M. Madiman), Birkhäuser (2019)Cones generated by random points on half-spheres and convex hulls of Poisson point processes
jointly with Zakhar Kabluchko, Alexander Marynych and Daniel Temesvari
Probability Theory and Related Fields 175, 1021–1061 (2019)Gaussian fluctuations for high-dimensional random projections of ℓpn-balls
jointly with David Alonso-Gutiérrez and Joscha Prochno
Bernoulli 25, 3139-3174 (2019)The isotropic constant of random polytopes with vertices on convex surfaces
jointly with Joscha Prochno and Nicola Turchi
Journal of Complexity 54, article 101394 (2019)Splitting tessellations in spherical spaces
jointly with Daniel Hug
Electronic Journal of Probability 24, article 24 (2019), 60 pagesHigh-dimensional limit theorems for random vectors in ℓpn-balls
jointly with Zakhar Kabluchko and Joscha Prochno
Communications in Contemporary Mathematics 21, article 1750092 (2019), 30 pagesExpected intrinsic volumes and facet numbers of random beta-polytopes
jointly with Zakhar Kabluchko and Daniel Temesvari
Mathematische Nachrichten 292, 79-105 (2019)
Download of the Mathematica notebooks: Random Beta-Polytopes, Random Beta'-PolytopesLimit theorems for random simplices in high dimensions
jointly with Julian Grote and Zakhar Kabluchko
ALEA Latin American Journal of Probability and Mathematical Statistics 16, 141–177 (2019)Poisson approximation of the length spectrum of random surfaces
jointly with Bram Petri
Indiana University Mathematics Journal 67, 1115-1141 (2018)Gaussian polytopes: a cumulant-based approach
jointly with Julian Grote
Journal of Complexity 47, 1-41 (2018), Best Paper Award 2018Central limit theorem for the volume of random polytopes with vertices on the boundary
Discrete and Computational Geometry 59, 990-1000 (2018)Large deviations for high-dimensional random projections of ℓpn-balls
jointly with David Alonso-Gutiérrez and Joscha Prochno
Advances in Applied Mathematics 99, 1-35 (2018)Random polytopes: variances and central limit theorems for intrinsic volumes
jointly with Nicola Turchi and Florian Wespi
Proceedings of the American Mathematical Society 146, 3063–3071 (2018)Concentration and moderate deviations for Poisson polytopes and polyhedra
jointly with Julian Grote
Bernoulli 24, 2811-2841 (2018)Isotropic constant of random polytopes with vertices on an ℓp-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), 30 pagesA 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), 28 pagesBranching 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)
Publications 2010-2015
New Berry-Esseen bounds for non-linear functionals of Poisson random measures
jointly with Peter Eichelsbacher
Electronic Journal of Probability 19, article 102 (2014), 25 pagesMoments 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)
Publications before 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)
Unpublished manuscripts
A new quantitative central limit theorem on the Wiener space with applications to Gaussian processes
jointly with Tobias FisslerBirth-time distributions of weighted polytopes in STIT tessellations
jointly with Nguyen Ngoc LinhExact and asymptotic results for intrinsic volumes of Poisson k-flat processes
jointly with Matthias Schulte
My coauthors
David Alonso-Gutiérrez
Ehsan Azmoodeh
Anastas Baci
Andreas Basse O'Conner
Imre Bárány
Mareen Beermann
Florian Besau
Carina Betken
Gilles Bonnet
Richard Cowan
Emil Dare
Laurent Decreusefond
Christian Deuß
Peter Eichelsbacher
Tobias Fissler
Uta Freiberg
Hans-Otto Georgii (1944-2017)
Thomas Godland
Julian Grote
Jens Grygierek
Anna Gusakova
Nils Heerten
Johannes Heiny
Felix Herold
Christian Hirsch
Steven Hoehner
Julia Hörrmann
Daniel Hug
Zakhar Kabluchko
Tom Kaufmann
Markus Kiderlen
Julia Krecklenberg
Kai Krokowski
Ben Li
Günter Last
Christoph Leuenberger
Mathias Mørck Ljungdahl
Olexander Marynych
Kathrin Meier
Werner Nagel
Nguyen Ngoc Linh
Moritz Otto
Takashi Owada
Giovanni Peccati
Mathew D. Penrose
Bram Petri
Mark Podolskij
Joscha Prochno
Claudia Redenbach
Benedikt Rednoß
Anselm Reichenbachs
Matthias Reitzner
Daniel Rosen
Michael Roysdon
Holger Sambale
Tomasz Schreiber (1975-2010)
Matthias Schulte
Carsten Schütt
Mathias Sonnleitner
Daniel Temesvari
Nicola Turchi
Beatrice-Helen Vritsiou
Viola Weiß
Wolfgang Weil (1945-2018)
Elisabeth Werner
Florian Wespi
Joe Yukich
Dmitry Zaporozhets
Guangqu Zheng