Kevin Ren

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20242026

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math.MG2026

A threshold phenomenon for embeddings of Euclidean snowflakes and impossibility of dimension reduction

Assaf Naor, Kevin Ren

Fix $0 < θ ⩽ 1$ . We prove that if $1 ⩽ p ⩽ 2/ θ$ , then the $θ$ -snowflake of $ℓ_{2}^{k}$ , namely, $R^{k}$ equipped with the metric $((x,y)\in \mathbb{R}^k\t…

math.MG2024

Random zero sets with local growth guarantees

Alan Chang, Assaf Naor, Kevin Ren

We prove that if $(M, d)$ is an $n$ -point metric space that embeds quasisymmetrically into a Hilbert space, then for every $τ > 0$ there is a random subset $Z$ of…