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Musielak-Orlicz spaces that are isomorphic to subspaces of L1 (2015)
Journal Article
Prochno, J. (2015). Musielak-Orlicz spaces that are isomorphic to subspaces of L1. Annals of Functional Analysis, 6(1), 84-94. https://doi.org/10.15352/afa/06-1-7

We prove that 1/n! ∑π∈Gn (∑ni=1 |xiai,π(i)|2)1/2 is equivalent to a Musielak-Orlicz norm ||x||∑Mi. We also provide the converse result, i.e., given the Orlicz functions, we provide a formula for the choice of the matrix that generates the correspondi... Read More about Musielak-Orlicz spaces that are isomorphic to subspaces of L1.

On the Gaussian behavior of marginals and the mean width of random polytopes (2015)
Journal Article
Alonso-Gutiérrez, D., & Prochno, J. (2015). On the Gaussian behavior of marginals and the mean width of random polytopes. Proceedings of the American Mathematical Society, 143(2), 821-832. https://doi.org/10.1090/S0002-9939-2014-12401-4

© 2014 American Mathematical Society. We show that the expected value of the mean width of a random polytope generated by N random vectors (n ≤ N ≤ e√n) uniformly distributed in an isotropic convex body in ℝnis of the order√logNLK. This completes a r... Read More about On the Gaussian behavior of marginals and the mean width of random polytopes.

Uniform estimates for averages of order statistics of matrices (2015)
Journal Article
Lechner, R., Passenbrunner, M., & Prochno, J. (2015). Uniform estimates for averages of order statistics of matrices. Electronic Communications in Probability, 20, 1-12. https://doi.org/10.1214/ECP.v20-3992

We prove uniform estimates for the expected value of averages of order statistics of matrices interms of their largest entries. As an application, we obtain similar probabilistic estimates for ℓp norms via real interpolation.