Research interests
- Stochastic geometry and geometric probability
- Limit theorems for random geometric structures
- Random structures in high dimensions
- Malliavin calculus and Stein's method
- Asymptotic geometric analysis
- Convex and Integral geometry
Current teaching
Summer term 2022
- Probabilistic methods in geometry
days and times: tba - Convex and integral geometry, part II (jointly with Daniel Rosen)
day and time: tba - Graduate seminar on Probability and geometry
- SPP Research Seminar Ruhr: Interacting particle systems and random geometries
Winter term 2021/2022
- Mathematics III for computer scientists
Monday 10-12, HIB
Thursday 10-12, HZO30 - Convex and integral geometry (jointly with Daniel Rosen)
Wednesday 12-14, IA 1/63 - Graduate seminar on Probability and geometry
- SPP Research Seminar Ruhr: Interacting particle systems and random geometries
For my past teaching see here
Short CV
- Since 10|2016 I am full professor at Ruhr University Bochum
- From 04|2013 until 09|2016 I was junior professor at Ruhr University Bochum
- From 11|2012 until 03|2013 I was member in the group of Peter Eichelsbacher at Ruhr University Bochum and member of the SFB/TR-12
Symmetries and Universality in Mesoscopic Systems - From 10|2012 until 11|2012 I was guest in the group of Giovanni Peccati at Luxembourg University
- From 10|2010 until 09|2012 I was scientific assistant in the group of Matthias Reitzner at Osnabrück University
- In 09|2010 I got my PhD in Mathematics from the University of Fribourg (Switzerland) under the supervision of Andreas Bernig
- From 10|2007 until 09|2010 I was scientific assistant at the University of Fribourg (Switzerland)
- In 07|2007 I got my diploma in mathematics from the Friedrich-Schiller-University Jena under the supervision of Martina Zähle
Current and past projects
- I am one of the principal investigators in the DFG Priority Program (SPP) 2265 Random Geometric Systems.
- I am one of the principal investigators of the DFG Collaborative Research Centre/Transregio CRC/TRR 191 Symplectic Structures in Geometry, Algebra and Dynamics.
- I am one of the principal investigators in the DFG 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
- Bernoulli Journal
- Journal of Applied Probability and Advances in Applied Probability
- Elemente der Mathematik (Elements of Mathematics)
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, Ehsan Azmoodeh, Anastas Baci, Andreas Basse O'Conner, Imre Bárány, Mareen Beermann, Florian Besau, Carina Betken, Gilles Bonnet, Richard Cowan, Laurent Decreusefond, Christian Deuß, Peter Eichelsbacher, Tobias Fissler, Uta Freiberg, Hans-Otto Georgii (1944-2017), Thomas Godland, Julian Grote, Jens Grygierek, Anna Gusakova,Felix Herold, Julia Hörrmann, Daniel Hug, Zakhar Kabluchko, Tom Kaufmann, Kai Krokowski, Günter Last, Christoph Leuenberger, Mathias Mørck Ljungdahl, Alexander Marynych, Werner Nagel, Nguyen Ngoc Linh, Giovanni Peccati, Mathew D. Penrose, Bram Petri, Mark Podolskij, Joscha Prochno, Claudia Redenbach, Benedikt Rednoß, Anselm Reichenbachs, Matthias Reitzner, Daniel Rosen, Holger Sambale, Tomasz Schreiber (1975-2010), Matthias Schulte, Mathias Sonnleitner, Daniel Temesvari, Nicola Turchi, Beatrice-Helen Vritsiou, Viola Weiß, Wolfgang Weil (1945-2018), Elisabeth Werner, Florian Wespi, Marcus Wohler, Joe Yukich, Dmitry Zaporozhets, Guangqu Zheng
- Sharpening the probabilistic Arithmetic-Geometric Mean Inequality (jointly with Tom Kaufmann)
Preprint - Variance asymptotics and central limit theory for geometric functionals of Poisson cylinder processes (jointly with Carina Betken and Matthias Schulte)
Preprint - Weighted p-radial distributions on Euclidean and matrix p-balls with applications to large deviations (jointly with Tom Kaufmann)
Preprint - Beta-star polytopes and hyperbolic stochastic geometry (jointly with Thomas Godland and Zakhar Kabluchko)
Preprint - The β-Delaunay tessellation IV: Mixing properties and central limit theorems (jointly with Anna Gusakova and Zakhar Kabluchko)
Preprint - Optimal Variance-Gamma approximation on the second Wiener chaos (jointly with Ehsan Azmoodehsan and Peter Eichelsbacher)
Preprint - Random cones in high dimensions II: Weyl cones (jointly with Thomas Godland and Zakhar Kabluchko)
Preprint - The β-Delaunay tessellation II: The Gaussian limit tessellation (jointly with Anna Gusakova and Zakhar Kabluchko)
Preprint - Random cones in high dimensions I: Donoho-Tanner and Cover-Efron cones (jointly with Thomas Godland and Zakhar Kabluchko)
Preprint - A 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 (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 (2022+) - Limit theorems for random points in a simplex (jointly with Anastas Baci, Zakhar Kabluchko, Joscha Prochno and Mathias Sonnleitner)
Journal of Applied Probability (2021+) - Weak 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 (2021+) - 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 pages - A 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 pages - Does 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 ℓ_{p}^{n}-balls. II (jointly with Zakhar Kabluchko and Joscha Prochno)
Communications in Contemporary Mathematics 23, article 1950073 (2021), 35 pages - The 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 pages - Asymptotic 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 pages - Intersection 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 pages - Asymptotic 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 pages - Exact 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 pages - Sanov-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 pages - Gaussian fluctuations for edge counts in high-dimensional random geometric graphs (jointly with Jens Grygierek)
Statistics and Probability Letters 158, 108674 (2020) - Geometry of ℓ_{p}^{n}-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 ℓ_{p}^{n}-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 pages - High-dimensional limit theorems for random vectors in ℓ_{p}^{n}-balls (jointly with Zakhar Kabluchko and Joscha Prochno)
Communications in Contemporary Mathematics 21, article 1750092 (2019), 30 pages - Expected 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'-Polytopes - Limit 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 2018 - Central 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 ℓ_{p}^{n}-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 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), 30 pages - 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), 28 pages - 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), 25 pages - 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) - A new quantitative central limit theorem on the Wiener space with applications to Gaussian processes (jointly with Tobias Fissler)
Preprint - 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
- Workshop: New Perspectives and Computational Challenges in High Dimensions (jointly with Aicke Hinrichs, Joscha Prochno and Elisabeth Werner)
Oberwolfach Report 6/2020 (2020) - Mini-Workshop: Perspectives in High-dimensional Probability and Convexity (jointly with Joscha Prochno and Elisabeth Werner)
Oberwolfach Reports 14, 499-526 (2017) - Wie jedes Jahr ...
Chapter in Was wäre die Mathematik ohne die Wurzel?
Springer Spektrum (2017) - Geometry of iteration stable random tessellations
PhD Thesis 2010, University of Fribourg (Switzerland) - Fraktale Eigenschaften zufällig iterierter selbstähnlicher Mosaike
Diploma Thesis 2007, Friedrich-Schiller University Jena - Berechenbare Zahlen (jointly with Christoph Leuenberger)
Die Wurzel 09+10/11 - Fraktale Geometrie 1 - 4
Die Wurzel 09+10/07, 11/07, 12/07 & 09/09 - Der Satz von Pick
Die Wurzel 09+10/08 - Gleichwinklige n-Ecke und gleichseitige n-Ecke (jointly with Marcus Wohler)
Die Wurzel 07/05 - "Wie jedes Jahr ..."
Die Wurzel 12/03
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 IB E2/111
44780 Bochum
Germany
Phone: 0234 - 32 - 28988
Consultation-hour: only by appointment