Han Huang

activity

20162026

most citedRank of Sparse Bernoulli Matrices

2 citations · 5 across the 8 of their papers we have counts for

collaborators

14 papers

math.PR2026

Well-invertible column subsets of sparse matrices are rare

Han Huang, Mark Rudelson, Konstantin Tikhomirov

A random $n \times k$ matrix $S$ is an \emph{ $(r, α)$ -oblivious subspace injection} (OSI) if $E ∥ S^{⊤} x ∥_{2}^{2} = ∥ x ∥_{2}^{2}$ for every $x \in R^{n}$ , and for every fixed…

math.FA2026

Hardness of approximation of centered convex bodies by polytopes

Han Huang, Mark Rudelson

The distance between convex bodies $K, L \subseteq \R^n$ is defined as \[ d(K,L)= \inf \left\{ λ\ge 1: \ L-x \subseteq T (K-y) \subseteq λ(L-x) \right\}, \] where the infimum is…

math.NA2022★ 1 cited

Average-case analysis of the Gaussian Elimination with Partial Pivoting

Han Huang, Konstantin Tikhomirov

The Gaussian Elimination with Partial Pivoting (GEPP) is a classical algorithm for solving systems of linear equations. Although in specific cases the loss of precision in GEPP due…

math.PR2021

Shotgun assembly of unlabeled Erdos-Renyi graphs

Han Huang, Konstantin Tikhomirov

Given a positive integer $n$ , an unlabeled graph $G$ on $n$ vertices, and a vertex $v$ of $G$ , let $N_{G} (v)$ be the subgraph of $G$ induced by vertices of $G$ of distance at most on…

math.PR2021★ 1 cited

On Dimension-dependent concentration for convex Lipschitz functions in product spaces

Han Huang, Konstantin Tikhomirov

Let $n \geq 1$ , $K > 0$ , and let $X = (X_{1}, X_{2}, \dots, X_{n})$ be a random vector in $R^{n}$ with independent $K$ --subgaussian components. We show that for every $1$ --Lipschitz conve…

math.PR2020★ 2 cited

Rank of Sparse Bernoulli Matrices

Han Huang

Let $A_{n}$ be an $n \times n$ random matrix with i.i.d Bernoulli( $p$ ) entries. For a fixed positive integer $β$ , suppose $p$ satisfies $\frac{lo g ( n )}{n} \leq p \leq c_{β}$ whe…

cs.IT2019

Distribution of the minimal distance of random linear codes

Jing Hao, Han Huang, Galyna Livshyts +1

In this paper, we study the distribution of the minimal distance (in the Hamming metric) of a random linear code of dimension $k$ in $F_{q}^{n}$ . We provide quantitative estim…

math.PR2019

A remark on the smallest singular value of powers of Gaussian matrices

Han Huang, Konstantin Tikhomirov

Let $n, k \geq 1$ and let $G$ be the $n \times n$ random matrix with i.i.d. standard real Gaussian entries. We show that there are constants $c_{k}, C_{k} > 0$ depending only on $k$ such tha…

math.MG2018

Improved bounds for Hadwiger's covering problem via thin-shell estimates

Han Huang, Boaz A. Slomka, Tomasz Tkocz +1

A central problem in discrete geometry, known as Hadwiger's covering problem, asks what the smallest natural number $N (n)$ is such that every convex body in ${\mathbb R}…

math.MG2018★ 1 cited

Ulam Floating Body

Han Huang, Boaz A. Slomka, Elisabeth M. Werner

We study a new construction of bodies from a given convex body in $R^{n}$ which are isomorphic to (weighted) floating bodies. We establish several properties of this new c…

math.MG2017

Approximations of convex bodies by measure-generated sets

Han Huang, Boaz A. Slomka

Given a Borel measure $μ$ on $R^{n}$ , we define a convex set by \[ M(μ)=\bigcup_{\substack{0\le f\le1,\\ \int_{{\mathbb R}^{n}}f\,{\rm d}μ=1 } }\left\{ \int_{{\mathbb R}^…

math.MG2017

John's Position is not good for approximation

Han Huang

Recall that a convex body $K$ is in John's position if the unit Euclidean ball is the maximal volume ellipsoid contained in $K$ . Approximating convex body in John's position by pol…

math.FA2016

Upper bound for the Dvoretzky dimension in Milman-Schechtman theorem

Han Huang, Feng Wei

For a symmetric convex body $K \subset R^{n}$ , the Dvoretzky dimension $k (K)$ is the largest dimension for which a random central section of $K$ is almost spherical. A Dvoretz…

math.MG2016

John Ellipsoid and the Center of Mass of a Convex Body

Han Huang

It is natural to ask whether the center of mass of a convex body $K \subset R^{n}$ lies in its John ellipsoid $B_{K}$ , i.e., in the maximal volume ellipsoid contained in $K$ . T…