Kevin Ren

activity

20212026

collaborators

5 papers

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.FA2025

Euclidean embedding, randomized clustering, and Lipschitz extension for finite and doubling subsets of $L_{p}$ when $p > 2$

Assaf Naor, Kevin Ren

Fix $p > 2$ . We prove that the Euclidean distortion of every $n$ -point subset of $L_{p}$ is $p^{3} (lo g n)^{\frac{1}{2} + o (1)}$ , thus, in particular, demonstrating that all $n$ -point subsets…

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…

math.CA2024

Radial Projections in $R^{n}$ Revisited

Paige Bright, Yuqiu Fu, Kevin Ren

We generalize the recent results on radial projections by Orponen, Shmerkin, Wang using two different methods. In particular, we show that given $X, Y \subset R^{n}$ Borel set…

math.CA2021

An incidence estimate and a Furstenberg type estimate for tubes in $R^{2}$

Yuqiu Fu, Shengwen Gan, Kevin Ren

We study the $δ$ -discretized Szemerédi-Trotter theorem and Furstenberg set problem. We prove sharp estimates for both two problems assuming tubes satisfy some spacing condition. Fo…

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

Euclidean embedding, randomized clustering, and Lipschitz extension for finite and doubling subsets of Lp​ when p>2

Random zero sets with local growth guarantees

Radial Projections in Rn Revisited

An incidence estimate and a Furstenberg type estimate for tubes in R2

Euclidean embedding, randomized clustering, and Lipschitz extension for finite and doubling subsets of $L_{p}$ when $p > 2$

Radial Projections in $R^{n}$ Revisited

An incidence estimate and a Furstenberg type estimate for tubes in $R^{2}$