Jun 6, 2024 · Let X be a finite-dimensional normed space. We prove that if the Hamming cube {-1,1}ⁿ embeds into X with bi-Lipschitz distortion at most D ≥ 1, ...

Dimensionality of Hamming Metrics and Rademacher Type. The biased measure. For α ∈ (0, 1), consider the α-biased probability measure µα on {−1, 1} given by ...

Nov 6, 2023 · The purpose of the present paper is to investi- gate certain metric properties of the Hamming cube via heat flow methods. 1.1. Dimensionality of ...

Oct 3, 2023 · The purpose of the present paper is to investi- gate certain metric properties of the Hamming cube via heat flow methods. with p-smoothness ...

Oct 3, 2023 · We present two geometric applications of heat flow methods on the discrete hypercube \{-1,1\}^n. First, we prove that if X is a finite-dimensional normed space,

We introduce the notion of the scaled Enflo type of a metric space, and show that for Banach spaces, scaled Enflo type p is equivalent to Rademacher type p.

Apr 3, 2020 · The hope was that maybe Enflo type is the “correct” extension of Rademacher type for metric spaces, and if so then it could be that many good ...

We introduce the notion of cotype of a metric space, and prove that for. Banach spaces it coincides with the classical notion of Rademacher cotype.

Dec 6, 2011 · This remarkable rigidity theorem guarantees that finite-dimensional properties are determined up to isomorphism by the metric structure of the ...

We will present below an argument that leads to the following slightly weaker fact: if a Banach space has Rademacher type p then for every ε ∈ (0,1) it also has ...