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math.PR2024
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…
math.PR2024
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\…
math.PR2024★ 1 cited
Gaussian statistics for left and right eigenvectors of complex non-Hermitian matrices
Sofiia Dubova, Kevin Yang, Horng-Tzer Yau +1
We consider a constant-size subset of left and right eigenvectors of an i.i.d. complex non-Hermitian matrix associated with the eigenvalues with pairwise distances at l…