Theo McKenzie

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20222024

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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 $d$ -regular graph on $N$ vertices with any fixed degree $d \geq 3$ and denote its eigenvalues as $λ_1=d/\sqrt{d-1}\geq λ_2\ge…

math.PR2023

The Spectral Edge of Constant Degree Erdős-Rényi Graphs

Ella Hiesmayr, Theo McKenzie

We show that for an Erdős-Rényi graph on $N$ vertices with expected degree $d$ satisfying $lo g^{- 1/9} N \leq d \leq lo g^{1/40} N$ , the largest eigenvalues can be precisely determined…