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Publications

 Here is a list of my collaborators:

Radosław Adamczak (Warsaw, Poland), David Alonso-Gutiérrez (Zaragoza, Spain), 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), Aicke Hinrichs (Linz, Austria), Julia Hörrmann (Bochum, Germany), Zakhar Kabluchko (Münster, Germany), David Krieg (Jena, Germany), Richard Lechner (Linz, Austria), Alexander E. Litvak (Edmonton, Canada), Erich Novak (Jena, Germany), Markus Passenbrunner (Linz, Austria), Stiene Riemer (Kiel, Germany), Carsten Schütt (Kiel, Germany), 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. Berry-Esseen bounds for random projections of lpn-balls (with S. Johnston)
    Preprint (2019)
  2. A new look at random projections of the cube and general product measures (with Z. Kabluchko, C. Thäle)
    Preprint (2019)
  3. Random sections of ellipsoids and the power of random information (with A. Hinrichs, D. Krieg, E. Novak, M. Ullrich)
    Preprint (2019)
  4. Exact asymptotic volume and volume ratio of Schatten unit balls (with Z. Kabluchko, C. Thäle)
    Preprint (2018)
  5. Intersections of unit balls in classical matrix ensembles (with Z. Kabluchko, C. Thäle)
    Israel J. Math. (2019+)
  6. High-dimensional limit theorems for random vectors in lpn-balls. II (with Z. Kabluchko, C. Thäle)
    Commun. Contemp. Math. (2019+)
  7. On the power of random information (with A. Hinrichs, D. Krieg, E. Novak, M. Ullrich)
    Multivariate Algorithms and Information-based Complexity, Radon Series (2019+)
  8. Sanov-type large deviations in Schatten classes (with Z. Kabluchko, C. Thäle)
    Ann. Inst. H. Poincaré Probab.Statist. (2019+)
  9. Embeddings of Orlicz-Lorentz spaces into L1
    St. Petersb. Math. J. (2019+)
  10. Yet another remark on the arithmetic-geometric mean inequality (with Z. Kabluchko, V. Vysotskiy)
    Studia Math. (2019+)
  11. The isotropic constant of random polytopes on surfaces of convex bodies (with C. Thäle, N. Turchi)
    J. Complexity (2019+)
  12. Curse of dimensionality for numerical integration on general domains (with A. Hinrichs, M. Ullrich)
    J. Complexity 50, 25-42 (2019)
  13. Gaussian fluctuations for high-dimensional random projections of lpn-balls (with D. Alonso-Gutiérrez, C. Thäle)
    Bernoulli (2018+)
  14. On the minimal k-dispersion of point sets in high dimensions (with A. Hinrichs, M. Ullrich, J. Vybíral)
    J. Complexity 51, 68-78 (2019)
  15. Phenomena in High-Dimensions (with C. Thäle, B.-H. Vritsiou)
    Snapshots of Modern Mathematics (2019+)
  16. Geometry of lpn-balls: classical results & recent developments (with C. Thäle, N. Turchi)
    High Dimensional Probability VIII, Progress in Probability, Birkhäuser (2019+)
  17. On almost everywhere convergence of tensor product spline projections (with M. Passenbrunner)
    Mich. Math. J. 68(1), 3-17 (2019)
  18. High-dimensional limit theorems for random vectors in lpn-balls (with Z. Kabluchko, C. Thäle)
    Commun. Contemp. Math. 21(1), 1-30 (2019)
  19. Large deviations for high-dimensional random projections of lpn-balls (with D. Alonso-Gutiérrez, C. Thäle)
    Adv. Appl. Math. 99, 1-35 (2018)
  20. 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)
  21. Entropy numbers of embeddings of Schatten classes  (with A. Hinrichs, J. Vybíral)
    J. Funct. Anal. 273(10), 3241-3261 (2017)
  22. Estimating averages of order statistics of bivariate functions (with R. Lechner, M. Passenbrunner)
    J. Theor. Probab. 30(4), 1445-1470 (2017)
  23. The geometry of random convex sets between polytopes and zonotopes (with D. Alonso-Gutiérrez)
    J. Math. Anal. Appl. 450(1), 670-690 (2017)
  24. 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)
  25. 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)
  26. Mean width of random perturbations of random polytopes (with Alonso-Gutiérrez)
    Adv. Geom. 17(1), 75-90 (2017)
  27. Probabilistic estimates for tensor products of random vectors (with D. Alonso-Gutiérrez, M. Passenbrunner)
    Proc. Amer. Math. Soc. 144(5), 2133-2148 (2016)
  28. Uniform estimates for averages of order statistics of matrices (with R. Lechner, M. Passenbrunner)
    Electron. Commun. Probab. 20(4), 1-12 (2015)
  29. 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)
  30. Musielak-Orlicz spaces that are isomorphic to subspaces of L1
    Ann. Funct. Anal. 6(1), 84-94 (2015)
  31. 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)
  32. 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)
  33. Estimating support functions of random polytopes via Orlicz norms} (with D. Alonso-Gutiérrez)
    Discret. Comput. Geom. 49(3), 558-588 (2013)
  34. A combinatorial approach to Musielak-Orlicz spaces
    Banach J. Math. Anal. 7(1), 132-141 (2013)
  35. On the maximum of random variables on product spaces (with S. Riemer)
    Houst. J. Math. 39(4), 1301-1311 (2013)
  36. Ein erstaunliches Schnur-Orakel (with M. Schmitz),
    Stochastik in der Schule 33(1), 2-7 (2013)
  37. Combinatorial inequalities and subspaces of L1 (with C. Schütt)
    Studia Math. 211(1), 21-39 (2012)
  38. Subspaces of L1 and Combinatorial Inequalities in Banach Space Theory
    Doctoral thesis (2011)


Work in progress

  • The geometry of Schatten classes
  • High-dimensional random projections of lpn-balls: between large deviations and gaussian fluctuations (with D. Alonso-Gutiérrez, C. Thäle)
  • On operator norms of Gaussian random matrices (with R. Adamczak)
  • A central limit theorem for high-dimensional sections and projections of lp-balls (with Z. Kabluchko, C. Thäle) 
  • Gelfand numbers of embeddings between Schatten p-classes (with A. Hinrichs, J. Vybíral)
  • Large deviations for the volume of the projected cube (with Z. Kabluchko)

Kontakt

Dipl.-Math. Dr. rer. nat.

Joscha Prochno

Heinrichstraße 36
8010 Graz
Austria

Telefon:+43 (0)316 380 - 5177

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