Vector-valued concentration inequalities on the biased discrete cube
Abstract
We present vector-valued concentration inequalities for the biased measure on the discrete cube { − 1 , 1 } n with an optimal dependence on the bias parameter and the Rademacher type of the target Banach space. These results allow us to obtain novel vector-valued concentration inequalities for the measure given by a product of Poisson distributions. We further obtain lower bounds on the average distortion with respect to the biased measure of embeddings of the hypercube into Banach spaces of nontrivial type which imply average non-embeddability.
Fields of Study & Subjects
Point processes and geometric inequalities
Random Matrices and Applications
Advanced Banach Space Theory
Publication details
- Journal / source
- Journal of Functional Analysis
- Volume
- 290
- Issue
- 7
- Pages
- 111334–111334
- Publication date
- 6 January 2026
- Language
- EN