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math.SP2024
The spectral concentration for damped waves on compact Anosov manifolds
Yulin Gong
We study the spectral distribution of damped waves on compact Anosov manifolds. Sjöstrand \cite{SJ1} proved that the imaginary parts of the majority of the eigenvalues concentrate…
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…