Work

Vector-valued concentration inequalities on the biased discrete cube

Year: 2026

Type: article

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.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2025.111334

Author: Miriam Gordin

Institution: Princeton University

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250

Funder: National Science Foundation