The Second-Order Threshold for Standardized Laplacian Eigenvalues
Year: 2026
Type: article
Abstract: Chebotarev conjectured that at and above a chord-weight threshold, each pair of conjugate Fourier modes contributes nonpositively to the second-order outward displacement of a circulant standardized Laplacian eigenvalue. We prove the inequality for every admissible order and show that it is strict above the threshold. The proof reduces the sum of coefficients to a weighted average of two real rational terms. A trigonometric bound on the product of their arguments determines the sign. The strict inequality also gives a local bound under perturbations of all arc weights, with equality only for the nearby circulants with uniform chord weights.
Authors: Li, Runheng, Ji, Jiashun
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225613169
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