3 papers
math.PR2026
The Gaussian Wave for Graphs of Finite Cone Type
Amir Dembo, Theo McKenzie
We show that for any infinite tree of finite cone type satisfying a mild expansion condition, the only typical process on its vertices with covariance induced by the Green's functi…
math.PR2025
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\…
math.SP2024
Arbitrary Spectral Edge of Regular Graphs
Dingding Dong, Theo McKenzie
We prove that for each and , the set of limit points of the first eigenvalues of sequences of -regular graphs is \[ \{(μ_1,\dots,μ_k): d=μ_1\geq \dots\…