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arXiv · 2004.01345

A note on pair dependent linear statistics with slowly growing variance

Ander Aguirre·Alexander Soshnikov
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Abstract

We prove Gaussian fluctuation for pair counting statistics of the form $ \sum_{1\leq i\neq j\leq N} f(\theta_i-\theta_j)$ for the Circular Unitary Ensemble (CUE) of random matrices in the case of a slowly growing variance in the limit of large $N.$

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Ander Aguirre, Alexander Soshnikov. 2020-04-03. A note on pair dependent linear statistics with slowly growing variance. https://doi.org/10.1134/s0040577920120090

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