8 papers
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…
Delocalization of Non-Mean-Field Random Matrices in Dimensions
Sofiia Dubova, Fan Yang, Horng-Tzer Yau +1
We study random band matrices with mean-zero complex Gaussian entries, where lie on the discrete torus i…
Delocalization of One-Dimensional Random Band Matrices
Horng-Tzer Yau, Jun Yin
Consider an Hermitian one-dimensional random band matrix with band width for any . In the bulk of the spectrum and in the l…
Delocalization of Two-Dimensional Random Band Matrices
Sofiia Dubova, Kevin Yang, Horng-Tzer Yau +1
We study a random band matrix of dimension with mean-zero complex Gaussian entries, where belong to the discrete torus $(\mathbb{Z}/\sqrt{N}\ma…
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 prese…
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\…