This seminar is part of the DFG project Limit theorems for the volume of random projections of lp balls which is jointly conducted by the probability team in Bochum and the functional analysis team at the University of Passau. The seminar takes place online on Thursday from 9.30 - 11.00, please send an e-Mail to Christoph Thäle if you would like to participate. The seminar continues in the summer term.
Our goal in this semester is to understand the relevance of the KLS conjecture and some recent progress around it. In addition, we want to give an access to the work of M. Talagrand who recently received the 2024 The seminar plan is as follows:
The KLS conjecture I
June 6, 2024, Philipp Tuchel
The KLS conjecture II
June 13, 2024, Tristan Schiller
Suprema of Gaussian processes I
June 20, 2024, Javier Martin Goni
Suprema of Gaussian processes II
June 27, 2024, Marco Krause
Suprema of Gaussian processes III
July 3, 2024, David Krieg
Suprema of Gaussian processes IV
July 14, 2024, Michael Juhos
Our goal in this semester is to read parts of the monograph Asymptotic Theory of Finite Dimensional Normed Spaces by V. Milman and G. Schechtman. The seminar plan is as follows:
The Haar measure
October 19, 2023, Marco Krause
The isoperimetric inequality on the sphere
November 2, 2023, Philipp Tuchel
Almost Euclidean subspaces of a normed space
November 16, 2023, Mathias Sonnleitner
Almost Euclidean subspaces of lpn spaces
November 30, 2023, Michael Juhos
Levy families
December 14, 2023, Tristan Schiller
C. Aistleitner, L. Frühwirth, J. Prochno: Diophantine conditions in the law of the iterated logarithm for lacunary systems
Probability Theory and Related Fields (2024)
Z. Kabluchko, J. Prochno, M. Sonnleitner: A probabilistic approach to Lorentz balls
To appear in Journal of Functional Analysis (2024+)
J. Prochno, M. Strzelecka: Moderate deviation principles and Mod-Gaussian convergence for lacunary trigonometric sums
Preprint
M. Juhos, L. Frühwirth, J. Prochno: The Maclaurin inequality through the probabilistic lens
Preprint
M. Sonnleitner, C. Thäle: A note on critical intersections of classical and Schatten p-balls
Preprint
J. Prochno: The large and moderate deviations approach in geometric functional analysis
Preprint
C. Schütt, N. Turchi, C. Thäle, E. Werner: Weighted floating functions and weighted functional affine surface areas
Preprint
J. Prochno, C. Schütt, M. Sonnleitner, E. Werner: Random approximation of convex bodies in Hausdorff metric
Preprint
J. Prochno, M. Sonnleitner, J. Vybíral: Entropy numbers of finite-dimensional Lorentz space embeddings
Preprint
M. Juhos, Z. Kabluchko, J. Prochno: Asymptotic theory of Schatten classes
Preprint
E. Dare, M. Kiderlen, C. Thäle: A Blaschke-Petkantschin formula for linear and affine subspaces with application to intersection probabilities
Preprint
J. Prochno, C. Thäle, P. Tuchel: Limit theorems for the volume of random projections and sections of lpn-balls