# Differential Identities for the Structure Function of Some Random Matrix Ensembles

@article{Forrester2020DifferentialIF,
title={Differential Identities for the Structure Function of Some Random Matrix Ensembles},
author={Peter J. Forrester},
journal={arXiv: Mathematical Physics},
year={2020}
}
• P. Forrester
• Published 1 June 2020
• Mathematics
• arXiv: Mathematical Physics
The structure function of a random matrix ensemble can be specified as the covariance of the linear statistics $\sum_{j=1}^N e^{i k_1 \lambda_j}$, $\sum_{j=1}^N e^{-i k_2 \lambda_j}$ for Hermitian matrices, and the same with the eigenvalues $\lambda_j$ replaced by the eigenangles $\theta_j$ for unitary matrices. As such it can be written in terms of the Fourier transform of the density-density correlation $\rho_{(2)}$. For the circular $\beta$-ensemble of unitary matrices, and with $\beta$ even…
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