Xuanang Hu

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math.PR2026

Sharp singularity asymptotics for discrete random matrices

Xuanang Hu, Zeyan Song, Xinglong Wu

We resolve the Rademacher singularity conjecture: an $n \times n$ matrix with independent uniform ${- 1, 1}$ entries is singular with probability $(2 + o (1)) n^{2} 2^{- n}$ . More generally…

math.PR2026

Sharp Convex Concentration for Symmetric Random Tensors with Subgaussian Coordinates

Xuanang Hu

Let $X = (X_{1}, \dots, X_{n})$ have independent coordinates with mean zero, variance one, and $∥ X_{i} ∥_{ψ_{2}} \leq K$ , and let $H_{d} = (R^{n})^{\otimes_{2} d}$ . Let $L > 0$ and let $f:H_d\to…

math.PR2026

The Optimal Rate in the Averaged Random-Marginal Central Limit Theorem for Log-Concave Measures

Xuanang Hu

Let $X$ be a centered isotropic log-concave random vector in $R^{n}$ . For $θ \in S^{n - 1}$ , let $μ_{θ}$ be the law of $⟨ X, θ ⟩$ , and let $Θ$ be uniformly distributed…

math.PR2026

Uniform Concentration for $α$ -subexponential Random Operators

Tiankun Diao, Xuanang Hu, Vladimir V. Ulyanov +1

Random matrices acting on structured sets play a fundamental role in high-dimensional geometry, compressed sensing, and randomized algorithms. Existing results primarily focus on s…

math.PR2025

The Dual Majorizing Measure Theorem for Canonical Processes

Xuanang Hu, Vladimir V. Ulyanov, Hanchao Wang

We give a dual, separated-tree formulation of Latala's majorizing measure theorem for canonical processes with log-concave tails. Under the same assumptions as in Latala's characte…

math.PR2025

On Concentration Inequality of the Laplacian Matrix of Erdős-Rényi Graphs

Yiming Chen, Xuanang Hu, Pengtao Li

This paper focuses on the concentration properties of the spectral norm of the normalized Laplacian matrix for Erdős-Rényi random graphs. First, We achieve the optimal bound that c…

Sharp singularity asymptotics for discrete random matrices

Sharp Convex Concentration for Symmetric Random Tensors with Subgaussian Coordinates

The Optimal Rate in the Averaged Random-Marginal Central Limit Theorem for Log-Concave Measures

Uniform Concentration for α-subexponential Random Operators

The Dual Majorizing Measure Theorem for Canonical Processes

On Concentration Inequality of the Laplacian Matrix of Erdős-Rényi Graphs

Uniform Concentration for $α$ -subexponential Random Operators