Yukun He

collaborators

6 papers

math.PR2020

Fluctuations of extreme eigenvalues of sparse Erdős-Rényi graphs

Yukun He, Antti Knowles

We consider a class of sparse random matrices which includes the adjacency matrix of the Erdős-Rényi graph $G (N, p)$ . We show that if $N^{\varepsilon} \leq Np \leq N^{1/3-…

cs.LG2018

Efficient Two-Step Adversarial Defense for Deep Neural Networks

Ting-Jui Chang, Yukun He, Peng Li

In recent years, deep neural networks have demonstrated outstanding performance in many machine learning tasks. However, researchers have discovered that these state-of-the-art mod…

math.PR2018

Local law and complete eigenvector delocalization for supercritical Erdős-Rényi graphs

Yukun He, Antti Knowles, Matteo Marcozzi

We prove a local law for the adjacency matrix of the Erdős-Rényi graph $G (N, p)$ in the supercritical regime $pN \geq C lo g N$ where $G (N, p)$ has with high probability no isolated…

math.PR2018

Mesoscopic eigenvalue density correlations of Wigner matrices

Yukun He, Antti Knowles

We investigate to what extent the microscopic Wigner-Gaudin-Mehta-Dyson (WGMD) (or sine kernel) statistics of random matrix theory remain valid on mesoscopic scales. To that end, w…

math-ph2018

Diffusion Profile for Random Band Matrices: a Short Proof

Yukun He, Matteo Marcozzi

Let $H$ be a Hermitian random matrix whose entries $H_{x y}$ are independent, centred random variables with variances $S_{x y} = E ∣ H_{x y} ∣^{2}$ , where $x, y \in (\mathbb Z/L\ma…

math.PR2018

Mesoscopic linear statistics of Wigner matrices of mixed symmetry class

Yukun He

We prove a central limit theorem for the mesoscopic linear statistics of $N \times N$ Wigner matrices $H$ satisfying $E ∣ H_{ij} ∣^{2} = 1/ N$ and $E H_{ij}^{2} = σ / N$ , where…