"Mathematics is the most beautiful and most powerful creation of the human spirit."  Stefan Banach

Work in progress

• Large deviations for compact groups and multivariate projections of uniform distributions, with Z. Kabluchko

Submitted

• Large deviation behavior of lacunary sums, with L. Frühwirth and M. Juhos
• Random sections of lp-ellipsoids, optimal recovery, and Gelfand numbers of diagonal operators, with A. Hinrichs and M. Sonnleitner
  
• On the volume of intersections of p-ellipsoids, with M. Juhos
  
• Projections of the uniform distribution on the cube - a large deviation perspective, with Z. Kabluchko and S. Johnston
  
• On the spherical dispersion, with S. Breneis and D. Rudolf
• Approximation, Gelfand, and Kolmogorov numbers of Schatten class embeddings, with M. Strzelecki
  
• Limit theorems for the log-volume of random simplices from rotationally invariant distributions, with J. Heiny and S. Johnston
  
• Large deviations for lacunary sums, with C. Aistleitner, N. Gantert, Z. Kabluchko, and K. Ramanan
  
• Thin-shell concentration for random vectors in Orlicz balls via moderate deviations and Gibbs measures, with D. Alonso-Gutiérrez
  
• Sharp concentration for the largest and smallest piece in a k-regular self-similar fragmentation, with P. Dyszewski, N. Gantert, S. Johnston, and D. Schmid
  
• A Maxwell principle for generalized Orlicz balls, with S. Johnston
• Faà di Bruno's formula and inversion of power series, with S. Johnston
• Berry-Esseen bounds for random projections of lp-balls, with S. Johnston
  

To Appear

• Random sections of ellipsoids and the power of random information, Trans. Am. Math. Soc., to appear (2021+), with A. Hinrichs, D. Krieg, E. Novak, and M. Ullrich
• Gelfand numbers of embeddings of Schatten classes, Math. Ann., to appear (2021+), with A. Hinrichs and J. Vybíral
  
• Limit theorems for random points in a simplex, Adv. Appl. Probab., to appear (2021+), with A. Baci, Z. Kabluchko, M. Sonnleitner, and C. Thäle
  
• A new look at random projections of the cube and general product measures, Bernoulli, to appear (2021+), with Z. Kabluchko and C. Thäle
  

2021

• Large deviations, moderate deviations, and the KLS conjecture, J. Funct. Anal. 280 (1) (2021), 1-33, with D. Alonso-Gutiérrez and C. Thäle
  
• Statistical independence in mathematics - the key to a Gaussian law, Math. Semesterberichte 68 (1) (2021), 69-104, with G. Leobacher
  
• The maximum entropy principle and volumetric properties of Orlicz balls, J. Math. Anal. Appl. 495 (1) (2021), 1-19, with Z. Kabluchko
  
• High-dimensional limit theorems for random vectors in lp-balls. II, Commun. Contemp. Math. 23 (3) (2021), 3-17, with Z. Kabluchko and C. Thäle

2020

• Intersections of unit balls in classical matrix ensembles, Israel J. Math. 239 (1) (2020), 129-172, with Z. Kabluchko and C. Thäle
  
• Tractability properties of the discrepancy in Orlicz norms, J. Complexity 61 (2020), 1-9, with J. Dick, A. Hinrichs, and F. Pillichshammer
  
• Exact asymptotic volume and volume ratio of Schatten unit balls, J. Approx. Theory 257 (2020), 1-13, with Z. Kabluchko and C. Thäle
  
• On the power of random information, Radon Ser. Comput. Appl. Math. 27 (2020), 43-64, with A. Hinrichs, D. Krieg, E. Novak, and M. Ullrich
  
• Sanov-type large deviations in Schatten classes, Ann. Inst. H. Poincaré Probab. Statist. 56 (2) (2020), 928-953, with Z. Kabluchko and C. Thäle
  
• Embeddings of Orlicz-Lorentz spaces into L1, Algebra i Analiz 30 (1) (2020), 78-93
• Yet another note on the arithmetic-geometric mean inequality, Studia Math. 253 (1) (2020), 39-55, with Z. Kabluchko and V. Vysotskiy

2019

• The isotropic constant  of random polytopes on surfaces of convex bodies, J. Complexity 54 (2019), 1-17, with C. Thäle and N. Turchi
• Gaussian Fluctuations for high-dimensional random projections of lp-balls, Bernoulli 25 (4a) (2019), 3139-3174, with D. Alonso-Gutiérrez and C. Thäle
• On almost everywhere convergence of tensor product spline projections, Michigan. Math. J. 68 (1), 3-17 (2019), with M. Passenbrunner
• High-dimensional limit theorems for random vectors in lp-balls, Commun. Contemp. Math. 21 (1) (2019), 1-30, with Z. Kabluchko and C. Thäle
• Geometry of lp-balls: Classical results & recent developments, High Dimensional Probability VIII, Progress in Probability, Birkhäuser (2019+), with C. Thäle and N. Turchi
• On the minimal k-dispersion of point sets in high dimensions, J. Complexity 51 (2019), 68-78,with A. Hinrichs, M. Ullrich, J. Vybíral
  

2018

• Large deviations for high-dimensional random projections of lp-balls, Adv. Appl. Math. 99 (2018), 1-35, with D. Alonso-Gutierrez and C. Thäle
• Curse of dimensionality for numerical integration on general domains, J. Complexity 50 (2019), 25-42, with A. Hinrichs, M. Ullrich
• The isotropic constant of random polytopes with vertices on an lp-sphere, J. Geom. Anal. 28 (1) (2018), 405-426, with J. Hörrmann and C. Thäle

2017

• Entropy numbers of embeddings of Schatten classes, J. Funct. Anal. 273 (2017), 3241-3261, with A. Hinrichs and J. Vybíral
• On the geometry of projective tensor products, J. Funct. Anal. 273 (2) (2017), 471-495, with O. Giladi, C. Schütt, N. Tomczak-Jaegermann, and E. Werner
  
• On the geometry of random convex sets between polytopes and zonotopes, J. Math. Anal. Appl. 450 (1) (2017), 670-690 with D. Alonso-Gutiérrez
• On the expectation of operator norms of random matrices, Geometric Aspects of Functional Analysis, Lecture Notes in Math. 2169 (2017), 151-162, with O. Guédon, A. Hinrichs, and A. E. Litvak
• Mean width of random perturbations of random polytopes, Adv. Geom. 17 (1) (2017), 75-90, with D. Alonso-Gutiérrez

2016

• Estimating averages of order statistics of bivariate functions, J. Theor. Probab. (2016), 1-26, with R. Lechner and M. Passenbrunner

• Probabilistic estimates for tensor products of random vectors, Proc. Amer. Math. Soc. 144 (5) (2016), 2133-2148, with D. Alonso-Gutiérrez and M. Passenbrunner

2015

• Uniform estimates for averages of order statistics of matrices, Electron. Commun. Probab. 20 (27) (2015), 1-12, with R. Lechner and M. Passenbrunner
• On the gaussian behavior of marginals and the mean width of random polytopes, Proc. Amer. Math. Soc. 143 (2) (2015), 821-832, with D. Alonso-Gutiérrez
• Musielak-Orlicz spaces that are isomorphic to subspaces of L1, Ann. Funct. Anal. 6 (1) (2015), 84-94

2014

• On mean outer radii of random polytopes, Indiana Univ. Math. J. 63 (2) (2014), 579-595, with D. Alonso-Gutiérrez, N. Dafnis, and M. Hernandez Cifre

2013

• On the distribution of random variables corresponding to Musielak-Orlicz norms, Studia. Math. 219 (3) (2013), 269-287, with D. Alonso-Gutiérrez, S. Christensen, and M. Passenbrunner
• A combinatorial approach to Musielak-Orlicz spaces, Banach J. Math. Anal. 7 (1) (2013), 132-141
• Estimating support functions of random polytopes via Orlicz norms, Discrete Comput. Geom. 49 (3) (2013), 558-588, with D. Alonso-Gutiérrez
• On the maximum of random variables on product spaces, Houst. J. Math. 39 (4) (2013), 1301-1311, with S. Riemer
• Ein erstaunliches Schnur-Orakel, Stochastik in der Schule 33 (1) (2013), 2-7, with M. Schmitz

2012

• Combinatorial inequalities and subspaces of L1, Studia Math. 211 (1) (2012), 21-39, with C. Schütt

Theses

• High-dimensional probability & geometric functional analysis - contributions to the normal, moderate, and large deviations approach in geometric functional analysis and the geometry of Schatten classes (Habilitation treatise, 2021)
  
• Teilräume von L1 und kombinatorische Ungleichungen in der Banachraumtheorie (PhD thesis, 2011)
• Teilräume von Lp (Diploma thesis, 2008)