# 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} }

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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