Jiaoyang Huang

activity

20242026

collaborators

13 papers

math.PR2026

The oriented Kesten--McKay law for random regular digraphs

Yukun He, Jiaoyang Huang

We consider the adjacency matrix of a random directed $d$ -regular graph on $N$ vertices. For fixed $d \geq 2$ , we prove that the empirical eigenvalue density converges in probabilit…

math.PR2026

Loop Equations Characterize Random Matrix Statistics

Paul Bourgade, Jiaoyang Huang

We prove that the universal local point processes of random matrix theory are characterized by their loop equation hierarchies. More precisely, for every rational $β > 0$ , the $\math…

math.PR2026

Lecture Notes on Edge Universality for Random Regular Graphs

Jiaoyang Huang, Horng-Tzer Yau

The purpose of this note is to explain the structure, general strategy, and main ideas of the proof in the work of Huang, McKenzie, and Yau (2024) on the Ramanujan property and edg…

math.PR2025

Gaussian Waves and Edge Eigenvectors of Random Regular Graphs

Yukun He, Jiaoyang Huang, Horng-Tzer Yau

Backhausz and Szegedy (2019) demonstrated that the almost eigenvectors of random regular graphs converge to Gaussian waves with variance $0 \leq σ^{2} \leq 1$ . In this paper, we presen…

math.PR2025

Extremal eigenvectors of sparse random matrices

Yukun He, Jiaoyang Huang, Chen Wang

We consider a class of sparse random matrices, which includes the adjacency matrix of Erdős-Rényi graph $G (N, p)$ . For $N^{- 1 + o (1)} \leq p \leq 1/2$ , we show that the non-trivia…

math.PR2024

The Spectral Distribution of Random Graphs with Given Degree Sequences

Shuyi Wang, Kevin Li, Jiaoyang Huang

In this article, we study random graphs with a given degree sequence $d_{1}, d_{2}, \dots, d_{n}$ from the configuration model. We show that under mild assumptions of the degree sequenc…