Publications

 Here is a list of my collaborators:

Radosław Adamczak (Warsaw, Poland), Christoph Aistleitner (Graz, Austria), David Alonso-Gutiérrez (Zaragoza, Spain), Anastas Baci (Bochum, Germany), Sören Christensen (Hamburg, Germany), Nikos Dafnis (Vienna, Austria), Nina Gantert (Munich, Germany), Ohad Giladi (Newcastle, Australia), Olivier Guédon (Paris, France), María Hernández Cifre (Murcia, Spain), Johannes Heiny (Bochum, Germany), Aicke Hinrichs (Linz, Austria), Julia Hörrmann (Bochum, Germany), Samuel Johnston (Bath, UK) , Zakhar Kabluchko (Münster, Germany), David Krieg (Jena, Germany), Richard Lechner (Linz, Austria), Gunther Leobacher (Graz, Austria), Alexander E. Litvak (Edmonton, Canada), Erich Novak (Jena, Germany), Markus Passenbrunner (Linz, Austria), Kavita Ramanan (Providence, USA), Stiene Riemer (Kiel, Germany), Daniel Rudolf (Göttingen, Germany), Carsten Schütt (Kiel, Germany), Mathias Sonnleitner (Graz, Austria), Christoph Thäle (Bochum, Germany), Nicole Tomczak-Jaegermann (Edmonton, Canada), Nicola Turchi (Bochum, Germany), Mario Ullrich (Linz, Austria), Jan Vybíral (Prague, Czech Republic), Vladislav Vysotskiy (Brighton, UK), Elisabeth Werner (Cleveland, USA).

Here is a list of my publications. Most of them can also be found on arXiv.

  1. Approximation, Gelfand, and Kolmogorov numbers of Schatten class embeddings (with M. Strzelecki)
    Preprint (2021)
  2. Projections of the uniform distribution on the cube - a large deviation perspective (with Z. Kabluchko, S. Johnston)
    Preprint (2021)
  3. Sharp concentration for the largest and smallest fragment in a k-regular self-similar fragmentation (with P. Dyszewski, N. Gantert, S. Johnston, D. Schmid)
    Preprint (2021)
  4. The minimal spherical dispersion (with S. Breneis, D. Rudolf)
    Preprint (2021)
  5. Thin-shell theory for rotationally invariant random simplices (with J. Heiny, S. Johnston)
    Preprint (2021)
  6. Large deviations for lacunary sums (with C. Aistleitner, N. Gantert, Z. Kabluchko, K. Ramanan)
    Preprint (2020)
  7. A Maxwell principle for generalized Orlicz balls (with S. Johnston)
    Preprint (2020)
  8. Thin-shell concentration for random vectors in Orlicz balls via moderate deviations and Gibbs measures (with D. Alonso-Gutiérrez)
    Preprint (2020)
  9. Irrationality in school (with G. Leobacher)
    Preprint (2020)
  10. Faà di Bruno's formula and inversion of power series (with S. Johnston)
    Preprint (2019)
  11. Berry-Esseen bounds for random projections of lpn-balls (with S. Johnston)
    Preprint (2019)
  12. Random sections of ellipsoids and the power of random information (with A. Hinrichs, D. Krieg, E. Novak, M. Ullrich)
    Preprint (2019)
  13. Gelfand numbers of embeddings of Schatten classes (with A. Hinrichs, J. Vybíral)
    Math. Ann. (2021+)
  14. Limit theorems for random points in a simplex  (with A. Baci, Z. Kabluchko, M. Sonnleitner, C. Thäle)
    J. Appl. Probab. (2021+)
  15. A probabilistic way to discover the rainbow (with M. Schmitz)
    Math. Gaz. (2021+)
  16. A new look at random projections of the cube and general product measures (with Z. Kabluchko, C. Thäle)
    Bernoulli (2021+)
  17. The maximum entropy principle and volumetric properties of Orlicz balls (with Z. Kabluchko)
    J. Math. Anal. Appl. 495(1), 1-19 (2021)
  18. High-dimensional limit theorems for random vectors in lpn-balls. II (with Z. Kabluchko, C. Thäle)
    Commun. Contemp. Math. 23(3), 1-35 (2021)
  19. Large deviations, moderate deviations, and the KLS conjecture  (with D. Alonso-Gutiérrez, C. Thäle)
    J. Funct. Anal. 280(1), 1-33 (2021)
  20. Statistical independence in Mathematics - the key to a Gaussian law (with G. Leobacher)
    Math. Semesterberichte 68(1), 69–104 (2021)
  21. Intersections of unit balls in classical matrix ensembles (with Z. Kabluchko, C. Thäle)
    Israel J. Math. 239(1), 129-172 (2020)
  22. Tractability properties of the discrepancy in Orlicz norms (with J. Dick, A. Hinrichs, F. Pillichshammer)
    J. Complexity 61, 1-9 (2020)
  23. On the power of random information (with A. Hinrichs, D. Krieg, E. Novak, M. Ullrich)
    Multivariate Algorithms and Information-based Complexity, Radon Series 27, 43-64 (2020)
  24. Exact asymptotic volume and volume ratio of Schatten unit balls (with Z. Kabluchko, C. Thäle)
    J. Approx. Theory 257, 1-13 (2020)
  25. Embeddings of Orlicz-Lorentz spaces into L1
    St. Petersb. Math. J. 32(1), 78-93 (2020)
  26. Sanov-type large deviations in Schatten classes (with Z. Kabluchko, C. Thäle)
    Ann. Inst. H. Poincaré Probab.Statist. 56(2), 928-953 (2020)
  27. Yet another remark on the arithmetic-geometric mean inequality (with Z. Kabluchko, V. Vysotskiy)
    Studia Math. 253(1), 39-55 (2020)
  28. Curse of dimensionality for numerical integration on general domains (with A. Hinrichs, M. Ullrich)
    J. Complexity 50, 25-42 (2019)
  29. Gaussian fluctuations for high-dimensional random projections of lpn-balls (with D. Alonso-Gutiérrez, C. Thäle)
    Bernoulli 25(4a), 3139-3174 (2019)
  30. On the minimal k-dispersion of point sets in high dimensions (with A. Hinrichs, M. Ullrich, J. Vybíral)
    J. Complexity 51, 68-78 (2019)
  31. Phenomena in High-Dimensions (with C. Thäle, B.-H. Vritsiou)
    Snapshots of Modern Mathematics (2019)
  32. Geometry of lpn-balls: classical results & recent developments (with C. Thäle, N. Turchi)
    High Dimensional Probability VIII, Progress in Probability, Birkhäuser (2019+)
  33. The isotropic constant of random polytopes on surfaces of convex bodies (with C. Thäle, N. Turchi)
    J. Complexity 54, 1-17 (2019)
  34. On almost everywhere convergence of tensor product spline projections (with M. Passenbrunner)
    Mich. Math. J. 68(1), 3-17 (2019)
  35. High-dimensional limit theorems for random vectors in lpn-balls (with Z. Kabluchko, C. Thäle)
    Commun. Contemp. Math. 21(1), 1-30 (2019)
  36. Large deviations for high-dimensional random projections of lpn-balls (with D. Alonso-Gutiérrez, C. Thäle)
    Adv. Appl. Math. 99, 1-35 (2018)
  37. The isotropic constant of random polytopes with vertices on an lp-sphere (with J. Hörrmann, C. Thäle)
    J. Geom. Anal. 28(1), 405-426 (2018)
  38. Entropy numbers of embeddings of Schatten classes  (with A. Hinrichs, J. Vybíral)
    J. Funct. Anal. 273(10), 3241-3261 (2017)
  39. Estimating averages of order statistics of bivariate functions (with R. Lechner, M. Passenbrunner)
    J. Theor. Probab. 30(4), 1445-1470 (2017)
  40. The geometry of random convex sets between polytopes and zonotopes (with D. Alonso-Gutiérrez)
    J. Math. Anal. Appl. 450(1), 670-690 (2017)
  41. On the geometry of projective tensor products (with O. Giladi, C. Schütt, N. Tomczak-Jaegermann, E. Werner)
    J. Funct. Anal. 273(2), 471-495 (2017)
  42. On the expectation of operator norms of random matrices (with O. Guédon, A. Hinrichs, A. E. Litvak)
    GAFA Lecture Notes in Math. 2169, 151-162 (2017)
  43. Mean width of random perturbations of random polytopes (with Alonso-Gutiérrez)
    Adv. Geom. 17(1), 75-90 (2017)
  44. Probabilistic estimates for tensor products of random vectors (with D. Alonso-Gutiérrez, M. Passenbrunner)
    Proc. Amer. Math. Soc. 144(5), 2133-2148 (2016)
  45. Uniform estimates for averages of order statistics of matrices (with R. Lechner, M. Passenbrunner)
    Electron. Commun. Probab. 20(4), 1-12 (2015)
  46. On the gaussian behavior of marginals and the mean width of random polytopes (with D. Alonso-Gutiérrez)
    Proc. Amer. Math. Soc. 143(2), 821-832 (2015)
  47. Musielak-Orlicz spaces that are isomorphic to subspaces of L1
    Ann. Funct. Anal. 6(1), 84-94 (2015)
  48. On mean outer radii of random polytopes (with D. Alonso-Gutiérrez, N. Dafnis, M. A. Hernandez Cifre)
    Indiana Univ. Math. J. 63(2), 579-595 (2014)
  49. On the distribution of random variables corresponding to Musielak-Orlicz norms (with D. Alonso-Gutiérrez, S. Christensen, M. Passenbrunner)
    Studia Math. 219(3), 269-287 (2013)
  50. Estimating support functions of random polytopes via Orlicz norms (with D. Alonso-Gutiérrez)
    Discret. Comput. Geom. 49(3), 558-588 (2013)
  51. A combinatorial approach to Musielak-Orlicz spaces
    Banach J. Math. Anal. 7(1), 132-141 (2013)
  52. On the maximum of random variables on product spaces (with S. Riemer)
    Houst. J. Math. 39(4), 1301-1311 (2013)
  53. Ein erstaunliches Schnur-Orakel (with M. Schmitz),
    Stochastik in der Schule 33(1), 2-7 (2013)
  54. Combinatorial inequalities and subspaces of L1 (with C. Schütt)
    Studia Math. 211(1), 21-39 (2012)
  55. Subspaces of L1 and Combinatorial Inequalities in Banach Space Theory
    Doctoral thesis (2011)


Work in progress

  • The large deviation approach to geometric functional analysis
  • Asymptotic volume and volume ratio in Lorentz spaces (with Z. Kabluchko)
  • A fast Bobkov-Klartag-Sodin theorem (with S. Johnston)
  • The geometry of Schatten classes
  • On operator norms of Gaussian random matrices (with R. Adamczak)
  • Moderate deviations for the volume of random projections of the cube (with N. Gantert, C. Thäle)
  • A central limit theorem for high-dimensional sections and projections of lp-balls (with Z. Kabluchko, C. Thäle) 

  • Large deviations for compact groups and multivariate projections of uniform distributions on lp-balls (with Z. Kabluchko)

Kontakt

Dipl.-Math. Dr. rer. nat.

Joscha Prochno

Heinrichstraße 36
8010 Graz
Austria

+43 316 380 - 5177

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