13 papers · 1 filter
The oriented Kesten--McKay law for random regular digraphs
Yukun He, Jiaoyang Huang
We consider the adjacency matrix of a random directed -regular graph on vertices. For fixed , we prove that the empirical eigenvalue density converges in probabilit…
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 , the $\math…
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…
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 . In this paper, we presen…
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 . For , we show that the non-trivia…
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 from the configuration model. We show that under mild assumptions of the degree sequenc…
Ramanujan Property and Edge Universality of Random Regular Graphs
Jiaoyang Huang, Theo McKenzie, Horng-Tzer Yau
We consider the normalized adjacency matrix of a random -regular graph on vertices with any fixed degree and denote its eigenvalues as $λ_1=d/\sqrt{d-1}\geq λ_2\ge…
A convergence framework for Airy line ensemble via pole evolution
Jiaoyang Huang, Lingfu Zhang
The Airy line ensemble is an infinite sequence of random curves. It is a natural extension of the Tracy-Widom distributions, and is expected to be the universal edge scalin…
Extremal Eigenvalues of Random Kernel Matrices with Polynomial Scaling
David Kogan, Sagnik Nandy, Jiaoyang Huang
We study the spectral norm of random kernel matrices with polynomial scaling, where the number of samples scales polynomially with the data dimension. In this regime, Lu and Yau (2…
Asymptotics of Symmetric Polynomials: A Dynamical Point of view
Alice Guionnet, Jiaoyang Huang
In this paper we study the asymptotic behavior of the (skew) Macdonald and Jack symmetric polynomials as the number of variables grows to infinity. We characterize their limits in…
Fluctuations for non-Hermitian dynamics
Paul Bourgade, Giorgio Cipolloni, Jiaoyang Huang
We prove that under the Brownian evolution on large non-Hermitian matrices the log-determinant converges in distribution to a 2+1 dimensional Gaussian field in the Edwards-Wilkinso…
Optimal Eigenvalue Rigidity of Random Regular Graphs
Jiaoyang Huang, Theo McKenzie, Horng-Tzer Yau
Consider the normalized adjacency matrices of random -regular graphs on vertices with fixed degree , and denote the eigenvalues as $λ_1=d/\sqrt{d-1}\geq λ_2\geqλ_3\…
Fluctuation of the Largest Eigenvalue of a Kernel Matrix with application in Graphon-based Random Graphs
Anirban Chatterjee, Jiaoyang Huang
In this article, we explore the spectral properties of general random kernel matrices from a Lipschitz kernel with independent random v…