Spectral properties of a non-Hermitian extension of the diluted Wishart ensemble
Year: 2025
Type: article
Abstract: We develop a theoretical framework based on the cavity and replica methods to analyze the spectral properties of sparse asymmetric correlation matrices of the form F = ( X Y ⊤ + ω Y X ⊤ ) / 2 T , where X and Y are adjacency matrices of weighted Erdős–Rényi random graphs. We examine how the spectral density evolves as the asymmetry parameter ω varies from 0 < ω < 1 (nearly symmetric matrices) to − 1 < ω ⩽ 0 (nearly antisymmetric matrices). Analytical predictions are validated through exact numerical diagonalization, showing excellent agreement with theoretical results in the thermodynamic limit.
Source: Journal of Physics Complexity
Institutions: Hainan University, Universidad Autónoma Metropolitana
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,600
OpenAlex ID: W4417514375