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math.CO2024
Discrete trace formulas and holomorphic functional calculus for the adjacency matrix of regular graphs
Yulin Gong, Wenbo Li, Shiping Liu
We provide a unified method to study the adjacency matrices of regular graphs (including infinite ones) using holomorphic functional calculus. By applying this calculus on a specif…
math.CO2024
Spectral convergence of random regular graphs: Chebyshev polynomials, non-backtracking walks, and unitary-color extensions
Yulin Gong, Wenbo Li, Shiping Liu
In this paper, we give a short proof of the weak convergence to the Kesten-McKay distribution for the normalized spectral measures of random -lifts. This result is derived by ge…